Question

Is Rolle’s theorem applicable to f(x) = tan x on [ \(\frac {\pi }{4}, \frac {5\pi }{4}\) ]?

(a) Yes

(b) No

This question was posed to me in my homework.

Query is from Mean Value Theorem topic in section Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right answer is (b) No

Best explanation: Given function is f(x) = tan x on [ \(\frac {\pi }{4}, \frac {5\pi }{4}\) ]

F(x) = tan x is not defined at x on [ \(\frac {\pi }{4}, \frac {5\pi }{4}\) ]

So, f(x) is not continuous on [ \(\frac {\pi }{4}, \frac {5\pi }{4}\) ].

Hence, Rolle’s theorem is not applicable.