Problem 1E: Let f(x) = 7. Using the denition of the derivative, show that f(x) = 0 for all values of x. Problem 2E: Let f(x) = 17x+11. Use the denition of the derivative to calculate f(x). Problem 3E: For Exercises 35, determine if the derivative rules from this section apply. If they do, find the... Problem 4E: For Exercises 35, determine if the derivative rules from this section apply. If they do, find the... Problem 5E: For Exercises 35, determine if the derivative rules from this section apply. If they do, find the... Problem 6E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 7E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 8E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 9E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 10E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 11E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 12E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 13E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 14E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 15E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 16E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 17E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 18E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 19E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 20E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 21E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 22E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 23E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 24E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 25E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 26E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 27E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 28E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 29E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 30E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 31E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 32E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 33E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 34E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 35E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 36E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 37E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 38E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 39E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 40E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 41E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 42E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 43E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 44E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 45E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 46E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 47E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 48E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 49E: For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are... Problem 50E: In Exercises 5057, use the tangent line approximation. Given f(4) = 5, f(4) = 7, approximate... Problem 51E: In Exercises 5057, use the tangent line approximation. Given f(4) = 5, f(4) = 7, approximate... Problem 52E: In Exercises 5057, use the tangent line approximation. Given f(5) = 3, f(5) = 2, approximate... Problem 53E: In Exercises 5057, use the tangent line approximation. Given f(2) = 4, f(2) = 3, approximate... Problem 54E: In Exercises 5057, use the tangent line approximation. Given f(3) = 4, f(3) = 2, approximate... Problem 55E: In Exercises 5057, use the tangent line approximation. Given f(3) = 4, f(3) = 2, approximate... Problem 56E: In Exercises 5057, use the tangent line approximation. Given f(x)=x4x2+3, approximate f(1.04). Problem 57E: In Exercises 5057, use the tangent line approximation. Given f(x)=x3+x26, approximate f(0.97). Problem 58E: If f(x)=6x42x+7, find f(x), f(x), and f(x). Problem 59E: (a) Let f(x) = x7. Find f(x), f(x), and f(x). (b) Find the smallest n such that f (n)(x) = 0. Problem 60E: If p(t)=t3+2t2t+4, find d2p/dt2 and d3p/dt3. Problem 61E: If w(x)=x+(1/x), find d2w/dx2 and d3w/dx3. Problem 62E: For Problems 6267, determine if the derivative rules from this section apply. If they do, find the... Problem 63E: For Problems 6267, determine if the derivative rules from this section apply. If they do, find the... Problem 64E: For Problems 6267, determine if the derivative rules from this section apply. If they do, find the... Problem 65E: For Problems 6267, determine if the derivative rules from this section apply. If they do, find the... Problem 66E: For Problems 6267, determine if the derivative rules from this section apply. If they do, find the... Problem 67E: For Problems 6267, determine if the derivative rules from this section apply. If they do, find the... Problem 68E: If f(x)=(3x+8)(2x5), find f(x) and f(x). Problem 69E: Find the equation of the line tangent to the graph of f at (1, 1), where f is given by... Problem 70E: Find the equation of the line tangent to y=x2+3x5 at x = 2. Problem 71E: Find the equation of the line tangent to f(x) at x = 2, if f(x)=x3243x. Problem 72E: (a) Find the equation of the tangent line to f(x) = x3 at the point where x = 2. (b) Graph the... Problem 73E: (a) Use Figure 3.8 to rank the quantities f (1), f (0), f (1), f (4) from smallest to largest. (b)... Problem 74E: The graph of y=x39x216x+1 has a slope of 5 at two points. Find the coordinates of the points. Problem 75E: On what intervals is the graph of f(x)=x44x3 both decreasing and concave up? Problem 76E: For what values of x is the function y=x55x both increasing and concave up? Problem 77E: (a) Find the eighth derivative of f(x)=x7+5x54x3+6x7. Think ahead! (The nth derivative, f(n)(x), is... Problem 78E: For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative... Problem 79E: For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative... Problem 80E: For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative... Problem 81E: For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative... Problem 82E: With t in years since 2016, the height of a sand dune (in centimeters) is f(t) = 700 3t 2. Find... Problem 83E: A rubber balloon contains neon. As the air pressure, P (in atmospheres), outside the balloon... Problem 84E: A ball is dropped from the top of the Empire State building to the ground below. The height, y, of... Problem 85E: At a time t seconds after it is thrown up in the air, a tomato is at a height of f(t)=4.9t2+25t+3... Problem 86E: Let f(t) and g(t) give, respectively, the amount of water (in acre-feet) in two different reservoirs... Problem 87E: A jkulhlaup is the rapid draining of a glacial lake when an ice dam bursts. The maximum outflow... Problem 88E: (a) For y = kxn, show that near any point x = a, we have y/ynx/a. (b) Interpret this relationship in... Problem 89E: In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent... Problem 90E: In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent... Problem 91E: In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent... Problem 92E: In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent... Problem 93E: The depth, h (in mm), of the water runoff down a slope during steady rain3 is a function of the... Problem 94E: If M is the mass of the earth and G is a constant, the acceleration due to gravity, g, at a distance... Problem 95E: The period, T, of a pendulum is given in terms of its length, l, by T=2lg, where g is the... Problem 96E: (a) Use the formula for the area of a circle of radius r, A = r2, to find dAdr. (b) The result from... Problem 97E: Show that for any power function f(x) = xn, we have f(1) = n. Problem 98E: Suppose W is proportional to r3. The derivative dWdr is proportional to what power of r? Problem 99E: Given a power function of the form f(x) = axn, with f(2) = 3 and f(4) = 24, find n and a. Problem 100E: (a) Find the value of a making f(x) continuous at x = 1: f(x)={ax0x1x2+31x2. (b) With the value of a... Problem 101E: Let f(x)=x3+3x22x+1 and g(x)=x3+3x22x4. (a) Show that the derivatives of f(x) and g(x) are the same.... Problem 102E: Let f(x)=x43x2+1. (a) Show that f(x) is an even function. (b) Show that f (x) is an odd function.... Problem 103E: In Problems 103104, explain what is wrong with the statement. The only function that has derivative... Problem 104E: In Problems 103104, explain what is wrong with the statement. The derivative of f(x) = 1/x2 is f(x)... Problem 105E: In Problems 105107, give an example of: Two functions f(x) and g(x) such that ddx(f(x)+g(x))=2x+3. Problem 106E: In Problems 105107, give an example of: A function whose derivative is g(x) = 2 and whose graph has... Problem 107E: In Problems 105107, give an example of: A function which has second derivative equal to 6... Problem 108E: In Problems 108110, is the statement true or false? Give an explanation for your answer. The... Problem 109E: In Problems 108110, is the statement true or false? Give an explanation for your answer. The... Problem 110E: In Problems 108110, is the statement true or false? Give an explanation for your answer. If f(2) =... Problem 111E: In Problems 111112, is the statement true or false? You are told that f and g exist and that f and g... Problem 112E: In Problems 111112, is the statement true or false? You are told that f and g exist and that f and g... format_list_bulleted