The maximum value of the function `f(x)=((1+x)^(0. 6))/(1+x^(0. 6))` in the interval `[0,1]` is `2^(0. 4)` (b) `2^(-0. 4)` 1 (d) `2^(0. 6)`

For xgeq0 , the smallest value of the function f(x)=(4x^2+8x+13)/(6(1+x)), is

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

The number of solutions of the equation cos6x+tan^2x+cos(6x)tan^2x=1 in the interval [0,2pi] is (a) 4 (b) 5 (c) 6 (d) 7

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

If S_(1) and S_(2) are respectively the sets of local minimum and local maximum point of the function, f(x)=9x^(4)+12x^(3)-36x^(2)+25, x in R , then (a) S_(1)={-2}:S_(2)={0,1} (b) S_(1)={-2,0}:S_(2)={1} (c) S_(1)={-2,1}:S_(2)={0} (d) S_(1)={-1}:S_(2)={0,2}

Evaluate: int_0^2(dx)/((17+8x-4x^2)[e^(6(1-x))+1)

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

The function x^x decreases in the interval (0,e) (b) (0,1) (0,1/e) (d) none of these

The domain of the following function is f(x)=(log)_2(-(log)_(1/2)(1+1/((x^(1/4)))-1) (a) (0,1) (b) (1,0) (1,oo) (d) (1,oo)

If 2a+3b+6c=0, then prove that at least one root of the equation a x^2+b x+c=0 lies in the interval (0,1).