Consider the function f(x) = 3x³ – 6x on the interval - 4, 4|. Find the average or mean slope of the function - on this interval. By the Mean Value Theorem, we know there exists at least 4. 4) cuch that f' (a) ic e in th opon intorval (

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A: Q1)The function f(x)=x(x-6)^2satisfies both hypotheses of the Mean Value Theorem onthe interval…

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A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

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Q: s of f?

A: Given that: The graph derivative of f ' (x) of the function f :

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A: Dear student we are allow to solve first question only if you need rest of answere please upload…

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Q: b. Use the Second Derivative Test to find all local minima and local maxima for g(x).

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A: All the answers are given below

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A: Slope of tangent is obtained by derivative of the function f(x).

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A: Answer

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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: Find the average rate of change f(x) with respect to x on th4 interval of f(x)-X-5 (-1

A: The average rate of change of f(x) over an interval [a, b] is:

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Q: on the interval specified. g(x) = 4x3 − 3  on  [−3, 3]

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: