Question

Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals

`f(x)` = x – 2 log x, x ∈ [2, 7]

Answer 1

f(x) = x – 2 log x

f(x) = x – 2 log x

f(2) = 2 – 2 log 2 = 2 – log 4

f(7) = 7 – 2 log 7 = 7 – log 49

f(2) ≠ f(7)

So Rolle’s theorem is not applicable.