Differentiability Over An Interval

Differentiability in an Interval

Problems based on differentiability in an interval and oscillating limit

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

Monotonicity At A Point|Testing Of Monotonicity Of Differentiable Function At A Point|Exercise Questions|Monotonicity Over An Interval|Exercise Questions|Greatest And Least Value Of A Function|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)

PARAGRAPH : If function f,g are continuous in a closed interval [a,b] and differentiable in the open interval (a,b) then there exists a number c in (a,b) such that [g(b)-g(a)]f'(c)=[f(b)-f(a)]g'(c) If f(x)=e^(x) and g(x)=e^(-x) , a<=x<=b c=

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

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

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