5. Suppose that function f(x) satisfies f'(x) < 0, f (x) > 0 at interval [a, b], then the graph of y = f(x) ( ) over this interval. (A) increasing and concave upward (B) increasing and concave downward (C) decreasing and concave upward (D) decreasing and concave downward

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

A:

Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

A:

Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

A:

Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

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Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

A:

Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: Suppose the function f(x) has the derivative f'6): 4x-122 -8 こい x-) G。 C) what are the x-values of…

A: Here given derivative of function f(x) as f'x=4x-2x+12 (a) To find the critical point of function…

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

A:

Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: Let f(x)=x² – 3x'. For what value(s) of x in [–1, 1] is the slope of the line tangent to the graph…

A:

Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Develop a general rule for the nth derivative of xf(x), where f is a differentiable function of x.

A: Given: the function xfx, where f is a differentiable function of x.

Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

A:

Q: (a) Suppose that the first derivative of the function y = f (x) is given by f'(x) = 6(x +1)(x – 2)²…

A:

Q: 1. Suppose that the revenue (in dollars) from the sale of x units of a certain product is given by…

A: The revenue function is given by Rx = 70x-0.05x2 To evaluate: The expression of R'(x) using the…

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

A:

Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

A:

Q: Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does…

A: Given the first derivative is: y'=6x+1x-22

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

A:

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Consider the following function: fx=x2+2x Differentiate fx with respect to x: ddxfx=ddxx2+2xf'x=2x+2

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

A:

Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(x) = V5x +1. V5yl th)-…

A: Given; f(x)=√(5x+1)

Q: 1) Find the derivative of the given function with respects to 0 y = 3lan In 3

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: (2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where…

A:

Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

A:

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…

Q: suppose the derivative of f exists, and assume that f(2)=3, f'(2)=4. Let g(x)=x^2f(x) and h(x)=…

A: The objective is to find the equation of tangent lines of g(x) and h(x) at x=2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.