If , where c 0, show that , where 0

Question

If , where c > 0, show that , where 0 < a < c < b.

Philoid · Accepted Answer

Given:

f(x)=x(1-log x)

Since the function is continuous as well as differentiable

So, there exists c such that

(b-a) log c=b(1-log b )-a(1-log a)

Hence proved.