Let f(x) = 18/x - 3x. %3D a. Find all points on the graph of f at which the tangent line is horizontal. 3 b. Find all points on the graph of f at which the tangent line has slope 2 -

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A: Given function: Used formulas: Chain rule of differentiation, Quotient rule of differentiation,…

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Q: Below is the graph of y = f'(x), where f'(x) is the derivative of f(x). + -3 -2 -1 1 2 3

A: Explanation:

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Q: Use the given graph to estimate the value of each derivative. y= f(x) 1 0, 1 (a) f'(-3) (b) f'(-2)…

A: Hence,  (a) f'(-3) = -1 (b) f'(-2) = 0 (c) f'(-1) = 0.6 (d) f'(0) = 1.5 (e) f'(1) = 3 (f) f'(2) = 0…

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A: Given that

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A: ddx3x2+4x-8x32Apply the Quotient Rule:  fg'=f '·g-g'·fg2=ddx3x2+4x-8x32-ddxx323x2+4x-8x322Solving,…

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A: Explanation: Given a function f(x) and point of tangency (x,y). Also given that, the tangent line…

Q: Find the derivative of the function. 11 m n'

A: To find the derivative of the given function here we can apply the division rule of differentiation.…

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A: we have to calculate the following

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A: Graph of the function given,we have to find derivative of the function.

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A: We will find f'(x) using the product rule and the chain rule.

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A: The given interval is [0,π] So, a=0, b= π

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A: We have to find the derivative of the given function

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A: given function :

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A: To find the slope of the tangent we find f'(x)

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A: To find the relative rate of change we have to find f ' (x) [first derivative of f(x)]

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A: If fx and gx are two differentiable function then according to product rule of the differentiation,…

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Q: for the function f(x)= √2x+3, estimate the instantaneous rate of change at x=5. use h value of 0.01

A: The instantaneous rate of change of f at x = a is f'(a), if it exists,

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Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

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Q: Let f(x)= e^x^2 . Find an equation of the line tangent to the graph of f at the point the (1,e).

A: Tangent to the graph,

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A: topic- derivative and equation of tangent line to function

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Q: Consider the following. f(x) = 4x2 + 9x – 17 %3D (a) Find the instantaneous rate of change of the…

A: Given: f(x)=4x2+9x-17

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A: Simplify f''(x):f''(x)=2x2-3x

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A: y = (x2 + 2)(x3 − 4x) = x5 + 2x3 - 4x3 - 8x = x5 - 2x3 - 8x Recall famous law of differentiation:…

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A: Integrate and pass that through given point for value of constant

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Q: Q9. For what values of x does the graph of f(x)=x-2sin(x) have a horizontal tangent? *

A: As per Bartlebys expert answering policy, we can only answer one question with its three subparts,…

Q: Find the average rate of change of f(x) = 9x from 1/2 to 1.

A: Find the average rate of change of f(x) = 9x from 1/2 to 1