Prove that the function are increasing for the given intervals: `f(x)=secx-cos e cx ,x in (0,pi/2)`

Prove that the function are increasing for the given intervals: f(x)=sinx+tanx-2x ,x in (0,pi/2)

Prove that the function are increasing for the given intervals: f(x)=e^x+sinx ,x in R^+

The function f(x)=sin^4x+cos^4x increasing in interval

Prove that the function f(x)=(log)_e x is increasing on (0,oo)dot

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sinx + cos x in the interval [0 , pi//2] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = e^(x) cos x in the interval [-pi//2 , pi//2] .

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

Prove that the function f given by f(x)=x-[x] us increasing in (0,1)dot

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sin 3x in the interval [0,pi] .