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Chapter 3: Q. 52 (page 249)

For each graph of f in Exercises 49–52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

Short Answer

Expert verified

The graph satisfies the mean value theorem and c=0.5, 1, 3.5

Step by step solution

01

Step 1. Given information

02

Step 2. Explanation

From graph,

f(0)=0.1f(4)=1

From MVT,

f'(c)=f(b)-f(a)b-a

f'(c)=f(4)-f(0)4-0

f'(c)=1-0.14

f'(c)=0.94

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Most popular questions from this chapter

Find the possibility graph of its derivative f'.

Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=x2+1x,[a,b]=[−3,2]

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

Restate Theorem 3.3 so that its conclusion has to do with

tangent lines.
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