# Let f(x)=3x2+5x−10. Answer the following questions.1. Find the average slope of the function ff on the interval [−1,1]. Average Slope: m =2.Verify the Mean Value Theorem by finding a number cc in (−1,1)(−1,1) such that f′(c)=m Answer: c=

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Let f(x)=3x2+5x−10. Answer the following questions.

1. Find the average slope of the function ff on the interval [−1,1].
Average Slope: m =

2.Verify the Mean Value Theorem by finding a number cc in (−1,1)(−1,1) such that f′(c)=m

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Step 1

1.

Result used:

Let f be defined on the closed interval [a, b]. The average slope of f between a and b is the quotient

Step 2

Consider the function, f(x)=3x2+5x-10.

Here a=–1 and b=1.

Compute the average slope using the above formula as follows.

Step 3

2.

Result used:

Suppose f(x) is a function which is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

Then there is a number c such...

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MathCalculus