The point in the interval `(0,2pi)` where `f(X) =e^(x)` sinx has maximum slope is

In the interval (0,pi), f(x)=sinx-x is

The abscissae of a point,tangent at which to the curve y=e^(x)sin x,x in[0,pi] has maximum slope is

[" Numbers of points in the interval "[0,pi]" where "f(x)=[2cos x]" is "],[" discontinuous is (where "[.]" represent greatest integer "],[" function) "]

Find the interval where f(x)=sinx,x in[0,2pi] increasing.

Find the interval in which f(x) = sinx + cos x. [x in [0, 2 pi]] increases.

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) = sinx + cos x in the interval [0 , pi//2] .

Consider the following statements : 1. The function f(x)=sinx decreases on the interval (0,pi//2) . 2. The function f(x)=cosx increases on the interval (0,pi//2) . Which of the above statements is/are correct ?