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.
The function satisfies the Mean value theorem and the value of c is 1.75.
The function is continuous and differentiable on . The Mean Value Theorem applies to this function on the interval .
The slope of the line from (0, f(0)) to is:
By the Mean Value Theorem, there must exist at least one point with role="math" localid="1648378574205"
We have to find the value of c with we solve it:
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