(a) Sketch the graph of the function f(x) = x'. (b) Use part (a) to graph the function g(x) = (x – 1)³ – 2.

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A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

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A: Given:  Function y=f(x) = |ln|x|| To Find: Graph of function f(x) Concept used: Consider the graph…

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A: To draw the graph of the derivative of the function

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Q: Q3:- A. Find the Gamma function of [(1) using definition

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: Consider a function y =f(t) with domain (0. 1, 4. 2). Use the graph of the derivative function,…

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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: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

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

Q: Use differentials and the graph of g′ to approximate                                      (a)…

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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: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: МАТ 115 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1) %3D с. f(x) d. f(x) = 4e*- x 3D20…

A: As per barlteby guideline for more than one sub question asked only first three are to be answered…

Q: Q2:A/ Consider the function f(x) = 11x+3 -what are the first and second derivatives? -what are the…

A: We will answer the first three subparts of the first question as per our guideline. Please resubmit…

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

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Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

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Q: Find the second derivative of the function. g(x) = 9/x + e6× In(x) g"(x) = %3D

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Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: 7–46 Find the derivative of the function. 8. F(x) = (1 + x + x²)9

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A: Given, Graph of the f'(x) is shown as:

Q: 1. Consider the function f(x) given by its graph at which the points C, E and H are the inflection…

A: Let's find.

Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: 1. Sketch the graph of the function 4x f(x) = x E (-00, 00) 1+4x² Be sure to calculate the local…

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Q: (0. §) Find the equation of the function f whose graph passes through the point and whose derivative…

A: you can clearly understand if you follow the below solution

Q: f (x) = x² + 2* – 100 Solve this question by the Fixed-point method on the topic of solution of…

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Q: 4)Find the inflection points of the function . f(x)=ln(x^(2)+1)

A: In this question we will find the point of inflection   we have given function   f(x)=ln(x2+1)…

Q: shows the graphs of the first and second derivatives of a function y = ƒ(x). Copy the picture and…

A: The graph of the function passes through the point P.   The graph of the first and second derivative…

Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

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Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

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Q: The graphs of the derivatives of the functions F, G & H are shown below. Which of the functions have…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: Find the third derivative f"" for the function f(x) = I-5

A: The first derivative of is given as: Also the derivative of a function in form of is: The given…

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

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: Let f be a function with first derivative given by f' (x) = (x + 1)(x – 2)(x – 3). At what values of…

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Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

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Q: 1) 2 a) Let f(x)=√x +4. Use the definition of the derivative to find f'(x). Find f'(5) by two…

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Q: Let g be a function that has derivative x(x – 3) (x – 5)e2" g'(x) = Does x=3 belong to a local…

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Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

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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: Compute the derivative function f'(x) algebraically. f(x) =x²-9 O a. f'(x)= 2x O b. f'(x)=2 O c.…

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Q: Find the derivative of the function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…