contestada

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.

Respuesta :

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)

[tex]c = e-1 \\[/tex] = 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 [tex]c[/tex]   such that

[tex]\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}[/tex]

You have to solve for [tex]c[/tex]  and get that

[tex]c = e-1 \\[/tex] = 1.71828

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