Differentiability in an Interval

Exercise Questions |Differentiability Over An Interval|Exercise Questions |OMR

Let f(x), be a function which is continuous in closed interval [0,1] and differentiable in open interval 10,1[ Show that EE a point c in]0,1[ such that f'(c)=f(1)-f(0)

Which of the following is differentiable in the interval (1,2)?

Find the number of points where the function f(x)=max|tanx|,cos|x|) is non-differentiable in the interval (-pi,pi) .

Let f(x) be defined on [-2,2[ such that f(x)={{:(,-1,-2 le x le 0),(,x-1,0 le x le 2):} and g(x)= f(|x|)+|f(x)| . Then g(x) is differentiable in the interval.

A function f is differentiable in the interval 0

Letfand g be differentiable on the interval I and let a, b in I,a lt b . Then

A function f(x) is, continuous in the closed interval [0,1] and differentiable in the open interval [0,1] prove that f'(x_(1))=f(1) -f(0), 0 lt x_(1) lt 1