T Diagnostic Tests 1 Functions And Limits 2 Derivatives 3 Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric Functions 4 Applications Of Differentiation 5 Integrals 6 Techniques Of Integration 7 Applications Of Integration 8 Series 9 Parametric Equations And Polar Coordinates 10 Vectors And The Geometry Of Space 11 Partial Derivatives 12 Multiple Integrals 13 Vector Calculus A Trigonometry B Sigma Notation C The Logarithm Defined As An Integral expand_more
4.1 Maximum And Minimum Values 4.2 The Mean Value Theorem 4.3 Derivatives And The Shapes Of Graphs 4.4 Curve Sketching 4.5 Optimization Problem 4.6 Newton's Method 4.7 Antiderivatives Chapter Questions expand_more
Problem 1E: Explain the difference between an absolute minimum and a local minimum. Problem 2E: Suppose f is a continuous function defined on a closed interval [a, b]. (a) What theorem guarantees... Problem 3E: For each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an... Problem 4E: For each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an... Problem 5E: Use the graph to state the absolute and local maximum and minimum values of the function. Problem 6E: Use the graph to state the absolute and local maximum and minimum values of the function. Problem 9E: Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. Absolute... Problem 7E: 710 Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. 7.... Problem 8E: 710 Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. 8.... Problem 10E: 710 Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. 10.... Problem 11E: (a) Sketch the graph of a function that has a local maximum at 2 and is differentiable at 2. (b)... Problem 12E: (a) Sketch the graph of a function on [1, 2] that has an absolute maximum but no local maximum. (b)... Problem 13E: (a) Sketch the graph of a function on [1, 2] that has an absolute maximum but no absolute minimum.... Problem 14E: (a) Sketch the graph of a function that has two local maxima, one local minimum, and no absolute... Problem 15E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 16E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 20E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 17E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 18E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 19E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 21E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 22E: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum... Problem 23E: Find the critical numbers of the function. f(x)=4+13x12x2 Problem 24E: Find the critical numbers of the function. f(x) = x3 + 6x2 15x Problem 25E: Find the critical numbers of the function. f(x) = 2x3 3x2 36x Problem 26E: Find the critical numbers of the function. f(x) = 2x3 + x2 + 2x Problem 27E: Find the critical numbers of the function. g(t) = t4 + t3 + t2 + 1 Problem 28E: Find the critical numbers of the function. g(t) = |3t 4| Problem 29E: Find the critical numbers of the function. g(y)=y1y2y+1 Problem 30E: Find the critical numbers of the function. h(p)=p1p2+4 Problem 31E: Find the critical numbers of the function. F(x) = x4/5(x 4)2 Problem 34E: Find the critical numbers of the function. g() = 4 tan Problem 33E: Find the critical numbers of the function. f() = 2 cos + sin2 Problem 32E: Find the critical numbers of the function. g(x) = x1/3 x2/3 Problem 35E: Find the critical numbers of the function. f(x) = x2e3x Problem 36E: Find the critical numbers of the function. f(x) = x2 ln x Problem 37E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 12 + 4x ... Problem 38E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 5 + 54x ... Problem 39E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 3x2 ... Problem 40E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x3 6x2 +... Problem 41E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 3x4 4x3 ... Problem 42E: Find the absolute maximum and absolute minimum values of f on the given interval. f (x) = (x2 1)3,... Problem 43E: Find the absolute maximum and absolute minimum values of f on the given interval. f(t)=t4t2, [1, 2] Problem 44E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=xx2x+1,[0,3] Problem 45E: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2cos t +... Problem 46E: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = t + cot... Problem 47E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=xex2/8, [1,... Problem 48E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x ln x,... Problem 49E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + x +... Problem 50E: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x 2 tan1... Problem 51E: If a and b are positive numbers, find the maximum value of f(x) = xa(1 x)b, 0 x 1. Problem 52E: Use a graph to estimate the critical numbers of f(x) = |x3 3x2 + 2 | correct to one decimal place. Problem 53E: (a) Use a graph to estimate the absolute maximum and minimum values of the function to two decimal... Problem 54E: (a) Use a graph to estimate the absolute maximum and minimum values of the function to two decimal... Problem 55E: (a) Use a graph to estimate the absolute maximum and minimum values of the function to two decimal... Problem 56E: (a) Use a graph to estimate the absolute maximum and minimum values of the function to two decimal... Problem 57E: Between 0C and 30C, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is given... Problem 58E: An object with weight W is dragged along a horizontal plane by a force acting along a rope attached... Problem 59E: A model for the U S average price of a pound of white sugar from 1993 to 2003 is given by the... Problem 60E: The Hubble Space Telescope was deployed April 24, 1990, by the space shuttle Discovery. A model for... Problem 61E: When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm... Problem 62E: Show that 5 is a critical number of the function g(x)=2+(x5)3 but g does not have a local extreme... Problem 63E: Prove that the function f(x)=x101+x51+x+1 has neither a local maximum nor a local minimum. Problem 64E: If f has a local minimum value at c, show that the function g(x) = f(x) has a local maximum value at... Problem 65E: Prove Fermats Theorem for the case in which f has a local minimum at c. Problem 66E: A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax3 + bx2 + cx + d,... format_list_bulleted