Question

Find ’C’ using Lagrange’s mean value theorem, if f(x) = e^x, a = 0, b = 1.

(a) e^e-1

(b) e-1

(c) log\(_e^{e+1}\)

(d) log\(_e^{e-1}\)

The question was asked in an internship interview.

I would like to ask this question from Mean Value Theorem in chapter Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right choice is (d) log\(_e^{e-1}\)

Easy explanation: Given f(x) = e^x, a = 0, b = 1

f’(c) = \(\frac {f(b)-f(a)}{b-a}\)

e^c = \(\frac {e-1}{1-0}\)

e^c = e – 1

C = log\(_e^{e-1}\)