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^+

Find the absolute maximum value and the absolute minimum value of the functions in the given intervals: f (x) = sin x + cos x , x in [0,pi]

Prove that f(x)=x-sinx is an increasing function.

The function sin^(4)x+cos^(4)x is increasing in the interval

Prove that the functions do not have maxima or minima: f(x) = e^(x)

Find the absolute extrema of the following functions on the given closed interval. f(x)=2cosx+sin2x,[0,pi/2]

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).

Prove that the function f(x)=x^(2)-2x-3 is strictly increasing in (2, infty)