Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln(x), [1, 5]

Answer 1

Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]

Explanation:

We are given that a function

`f(x)=ln(x)`

Interval [1,5]

The given function is defined on this interval.

Hypothesis of Mean Value Theorem:

(1) Function is continuous on interval [a,b]

(2)Function is defined on interval (a,b)

From the graph we can see that

The function is continuous on [1,5] and differentiable at(1,5).

Hence, the function satisfies the hypothesis of the Mean Value Theorem.