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

At what points in the interval [0,2 pi], does the function sin 2x attain its maximum value?

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) "]

The function f(x)=x^(2)e^(x) has maximum value

In the interval (0, (pi)/(2)) the function f (x) = cos ^(2) x is :

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

Verify the conditions of Rolle's Theorem in the following problems. In each case, find a point in the interval, where the derivative vanishes : sinx-sin2x" on "[0,pi]

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] .

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 ?