Draw sign diagrams for each of the following functions. (a) f(x) =-4(2x +3)(3– x) (b) S(x) =-3x(x-2y°(4–xy'(x+3) (4x +7)(5 - 2x) (x-1) (c) S(x) =

Q: On the interval –5 < x < 6, for how many values does f (x)(graphed below) have a derivative equal to…

A: Given:

Q: Question 1 ( Use the First Derivative Test to find the local maximum and minimum values of the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: In(3x) Given f(x) the derivative f' (x) is 3 O x3x 3 3 1 3x 3x

A: differentiate both sides with respect to x and solve the question. see 2nd step.

Q: Find all possible functions with the given derivative. y'=-5+7/x^2

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: Find all the higher derivatives of the function f(x) = (2x-5)°. f(x) = f'(x) = p"(x) =|

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Q: 1. Find the derivative of the following functions at an arbitrary point x: 8 a. f(x) = x3/2 b. f(x)…

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Q: Find the derivative of the following: 1. y=x(V1- x³ ) 1+x 2. у-. 1-x (x³+5) V4-x² 3. у — x*-x2+6 sin…

A:

Q: Find the first derivative of the function g(x) = V5 +x +4cos (2x).

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: The graph of the function y = f(x) passes through the point (-1, 1) and the line tangent to the…

A:

Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x

A: Given:          y=3x3-4xe-5x Let:  y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…

Q: Question 31 Compute the derivative function f' (x) algebraically. f (x) = -5x³ + 7 O f' (x) = –15x²…

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Q: b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1. 2. f(x) = 3. f(x) = csc x…

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Q: How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show…

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Q: Find the value of the derivative (if it exists) at each indicated extremum.       f(x) = −3x√(x + 1)

A:

Q: 2 3 1. Determine the derivative to y² = x³ + y² + 2xy

A: Given problem:- Determine the derivative to y2 = x3 + y3 + 2xy

Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: Find the indicated derivative for the function. h"(x) for h(x) = 2x "5 – 6x -8 h"(x) =

A:

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: 3. Use derivatives to find the critical points anc (a) f(x)= x³ – 9x2 + 24.x + 5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find an equation of the tangent line to the graph of the following function f at the specified…

A:

Q: The derivative of f(x) = 2 cos 2x is an odd function.

A: Odd function

Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A:

Q: f. y=In(x8+1)

A: We will solve the problem

Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: find the function with the given derivative whosegraph passes through the point P.39. ƒ′(x) = 2x -…

A: We have to find the function for the given derivative passes through the point P: f'x=2x-1, P0, 0…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x²;…

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Q: y = In (*+1) °(x+1), (x+2)3

A:

Q: Question 1 Apply the First Derivative Test to find the minimum value of f(x)=(2x^+2)/x² . Keep 4…

A: The given problem is to find the minimum value of the given function using the first derivative…

Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

A:

Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = (x +…

A: Given:fx=x+223

Q: Find the derivatives of the functions k(x) = x2 sec (1/x)

A:

Q: Find the function with the derivative f'(x) 3x = e whose graph passes through the point P| 0,

A:

Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: III. For each of the following functions, find the indicated derivative using the definition. Show…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.…

Q: 1 4. Use the definition of the derivative to compute f'(x) given f(x) = 2x 3

A: Given,          The function is fx=12x-3 .

Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: Compute the derivative function f' (x) algebraically. f (x) = -5x3 +7 O f' (x) = -15x O f' (x) =…

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Q: f(x) = In(x² + 1)

A:

Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

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Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): x²(x + 1),…

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Q: Find derivatives of the functions defined as follows: y = -4e-0.3x

A: Our Aim is to find the derivative of the function given below:-y=-4e-0.3x -(i)