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Alex
3 years ago
15

a. Determine whether the Mean Value Theorem applies to the function f (x )equals ln 15 xf(x)=ln15x on the given interval [1 comm

a e ][1,e]. b. If​ so, find or approximate the​ point(s) that are guaranteed to exist by the Mean Value Theorem.
Mathematics
1 answer:
ivolga24 [154]3 years ago
5 0

Answer:

(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

Step-by-step 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

\frac{1}{c} = \frac{\ln(15e)-\ln(15*1)}{e-1} = \frac{\ln(15e/15)}{e-1} = \frac{\ln(e)}{e-1} = \frac{1}{e-1}

You have to solve for c  and get that

c = e-1 \\ = 1.71828

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