If f(x) = ex, x Î \[0, 1], then a number 'c' of Lagrange's m... | MATH - ROLLE'S THEOREM, LAGRANGE'S MEAN VALUE THEOREM | SolveeIt | Solveeit

Today, August 18

Question

If f(x) = e^x, x Î [0, 1], then a number 'c' of Lagrange's mean value theorem is

A

log (e – 1)

B

log (e + 1)

C

log e

D

None

Answer

log (e – 1)

Explanation

Solution

Q f(x) = e^x which is continuous & differentiable function & f(0) ¹ f(1)

\ f '(3) = $\frac{f(1) - f(0)}{1 - 0}$ ̃ e^c = $\frac{e^{1} - 1}{1}$

̃ c = log_e(e – 1) ̃ c = log_e(e – 1)