In the interval `[0,1],` the function `x^(25)(1-x)^(75)` takes its maximum value at the point 0 (b) `1/4` (c) `1/2` (d) `1/3`

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

The maximum value of f(x)=x/(1+4x+x^2) is -1/4 (b) -1/3 (c) -1/6 (d) 1/6

The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.

The number of values of x where the function f(x)=cosx+cos(sqrt(2)x) attains its maximum is 0 (b) 1 (c) 2 (d) infinite

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

The first derivative of the function [cos^(-1)(sinsqrt((1+x)/2))+x^x] with respect to x at x=1 is (a) 3//4 (b) 0 (c) 1//2 (d) -1//2

If the function e^(-x) f(X) assumes its minimum in the interval [0,1] at x = 1//4 which of the following is true ?

On which of the following intervals is the function x^(100)+sinx-1 decreasing? (a) (0,pi/2) (b) (0,1) (c) (pi/2,pi) (d) none of these

The value of a for which the function f(x)=asinx+(1/3)sin3x has an extremum at x=pi/3 is 1 (b) -1 (c) 0 (d) 2