Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of the derivative of f(x) on the interval [-3, 3] is given below. y = f'(x) 1 -3 -2 -1 2 3 -1 (1) Given that f(-1) = 2, find the equation of the tangent line to y = f(x) at x = -1.

Q: A curve, y=f(x) passes through the point (1, −1)(1, −1) and the slope of the tangent at any x is…

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Q: If f(1) = 3, f'(1) = 4, g(2) = 2, and g'(2) = 8, find F'(1). F'(1) = ... NOTE: This problem is a bit…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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

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

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Q: Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of…

A: As per the instruction, we will be answering only question 2. Given: For (a), From the given…

Q: 1. Find an equation of the tangent line to the graph of the function at the given point. f\xl=In…

A: Solved below

Q: 1 What is the lineur is The slope of the line tangent to the graph y = cos x at the point x =…

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Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

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Q: QUESTION 2 Let f(x) be a function with second derivative of f"(x) =(x+8)(7x –11)(x – 13). Determine…

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Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

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Q: | If In(x² – 3y) = x – y + 3 and y(-2) = 1, find y (-2) by implicit differentiation. y(-2) = An…

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Q: In x se the second derivative test to find the local extrema for the function f (x) = x3 •

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Q: when in a derivative problem is e^( ) =0 and when is not?

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Q: Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes…

A: Given,

Q: Question 9 Suppose 8 (x) = sec-(x²), what is the derivative of g with respect to x? 2x A 8 (x) =…

A: We need to find derivative.

Q: 5. Suppose f(3) = -2, g(3) = 5, h(3) = –1, f'(3) = -4, g'(3) = 3, and h'(3) 2. Find the value of the…

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Q: 3. Let f(x) =x In(x – 3)+5. Find the equation of the line tangent to the graph of f at the point…

A: Given thatf(x)=xln(x2-3)+5f'(x)=ddxxln(x2-3)+5         =xddxln(x2-3)+ln(x2-3)ddx(x)+ddx(5)…

Q: Problem 5  Find the derivative of the following function using the Fundamental Theorem of Calculus.…

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Q: Consider the graph of the derivative of a function f, given below: 10- -10- Find: a) Critical points…

A: Authoring guidelines:…

Q: Use the definition of a derivative to find f'(x) and f"(x), when f(x) = 2/x. I got f'(x) = -2/x2,…

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Q: 2) Suppose the graph of f (x) and the graph of its derivative f '(x) are shown below. Find an…

A: From the graph of f(x) , at x=1, f(x)=1 From the graph of f'(x), at x=1, f'(x)=-2

Q: Problem 4  Find the derivative of the following function  F(x)=∫ (t^2)/(1+(7t^4))dt Upper limit of…

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

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Q: Problem 3 Let f(r) = x² + r. Use the limit definition of the derivative to compute f'(2). Find an…

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Q: Question 5 Find the derivative: y = (3x 2x) Va5 2x + 2 - - dy 27-14x5-30x2+36x-8 2Va5-2x+2 (3x-2)…

A: The given function is  y=(3x2-2x) sqrt(x5-2x+2).

Q: In 5 x+1 Find the derivative of y = logs ((*)) with respect to x-1 independent variable x.

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Q: Find an equation of the tangent line to the graph of the function at the given point.…

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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: (a) Let f(x)=√√2x+1. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: . Use Euler's method with a step of 0.1 to estimate f(2.5) if f(1)=-2 and the derivative of the…

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Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: 3. If f(-1) = 3, f'(-1) = 5, g(-1) = -1, gʻ(-1) = 2, let h(x) = f(x) g(x). Find an equation for the…

A: given: f(-1)=3, f'(-1)=5, g(-1)=-1 and g'(-1)=2 h(x)=f(x)g(x). we have to find the equation of the…

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

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: Let f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative of the following…

A: Recall:  Product Rule:   d dxf(x).g(x)=f(x).g'(x)+g(x).f'(x)   Given, derivative(x) = f(x) . g(x) +…

Q: 2) Suppose the graph of f (x) and the graph of its derivative f'(x) are shown below. Find an…

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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: Find the derivative of: y = 4x^2 – 1/x   y’ = 2x – x^(-2) y’ = x^(-1) + 8x y’ = 8x - x^(-2) y’ =…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Problem 2 Find dy/dx of y = x* at the point (2,4) by following a similar procedure: 1. Apply In() to…

A: Applying “ln” on both sides of equation and simplifying.

Q: Problem 1: Consider some arbitrary function f(x), whose value and whose derivative values of every…

A: Notice that g(x) is 0 at x=1.

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: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

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: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: 2, Problem 6. Below is the graph of the derivative of a function f(x). 1.2 0.8 y 0.4 -2.4 -1.6 -1.2…

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Q: Example 2. Find the derivative of the following with respect to x. x" +1. (iv) x-5 (i) x12 + 7, (ii)…

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Q: Problem 1: Consider some arbitrary function f(x), whose value and whose derivative values of every…

A: The following concepts are used to analyse the linear approximation of the function. The graph of a…