Question

a. Determine whether the Mean Value Theorem applies to the function f (x )equals ln 15 xf(x)=ln15x on the given interval [1 comma e ][1,e]. b. If​ so, find or approximate the​ point(s) that are guaranteed to exist by the Mean Value Theorem.

Answer 1

(a)

The function f is continuous at [1,e] and differentiable at (1,e), therefore

the mean value theorem applies to the function.

(b)

`c = e-1 \\` = 1.71828

Explanation:

(a)

The function f is continuous at [1,e] and differentiable at (1,e), therefore

the mean value theorem applies to the function.

(b)

You are looking for a point
`c` such that

`(1)/(c) = (\ln(15e)-\ln(15*1))/(e-1) = (\ln(15e/15))/(e-1) = (\ln(e))/(e-1) = (1)/(e-1)`

You have to solve for
`c` and get that

`c = e-1 \\` = 1.71828