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

The value of lim_(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is 4 (b) 1/2 (c) 2 (d) 1/4

The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is (A) 18^@ (B) 36^@ (C) 22.5^@ (D) 15^@

If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) at x=0 is 0 (b) 6 (c) 12 (d) 24

Greatest value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) 2 (c) 3 (d) 1/3

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is (a) 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x))=x (a) sqrt(2) (b) -sqrt(2) (c) 1 (d) -1

Let f(1)=-2a n df^(prime)(x)geq4. 2for1lt=xlt=6. The smallest possible value of f(6) is 9 (b) 12 (c) 15 (d) 19

If the function f(x)=x^4+b x^2+8x+1 has a horizontal tangent and a point of inflection for the same value of x then the value of b is equal to -1 (b) 1 (c) 6 (d) -6

If f: RvecR ,g(x)=f(x)+3x-1, then the least value of function y=g(|x|) is a. -9/4 b. -5/4 c. -2 d. -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