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

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

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 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] .

f(x) = sinx - sin2x in [0,pi]

If f (x) ={{:(xlog_(e)x",",x gt0),(0",",x=0):} ,thenconclusion of LMVT holds at x = 1 in the interval [0,a] for f(x), then [a^(2)] is equal to (where [.] denotes the greatest integer) "_______".

Write the interval in which f(x)=sinx+cosx ,\ \ x in [0,\ pi//2] is increasing.

Find the intervals in which f(x) = sin x - cos x , "where "0 lt x lt 2 pi is decreasing

Let f(x)= { x e^(a x),x lt=0;x+a x^2-x^3,x >0 where a is a positive constant. Find the interval in which f^(prime)(x) is increasing.

On the interval [-(pi)/(4) , (pi)/(4)] , the function f (x) = sqrt(1 + sin^(2) x) has a maximum value of