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Chapter 3: Q. 53 (page 249)

Determine whether or not each function f in Exercises 53鈥�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 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=x2+1x,[a,b]=[鈭�3,2]

Short Answer

Expert verified

f(x) isn't continuous and differentiable on the given interval.

Step by step solution

01

Step 1. Given information

f(x)=x2+1xfor a=-2 and b=3

02

Step 2. Proving Mean Value Theorem  

Since,

0鈭�[-3,2]

f(0)=02+10

f(0)=undefined

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Determine whether or not each function f in Exercises 53鈥�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 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

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