Function `g(x)=2f((x^(2))/(2))+f(6-x^(2))` for all `xepsilonR` is decreasing and `f^(``)(x)gt0` for all `xepsilonR` then complete set of values of x is

If f(x) is a differentiable function satisfying f^(')(x)lt2 for all xepsilonR and f(1)=2, then greatest possible integral value of f(3) is

If f(x) ge0 for all x, then f(2-x) is

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing on

Prove that function f(x) = {-2x^(3)+3x^(2)-6x+5,xlt0 -x^(2)-x+1, xge0 is decreasing for all x.

The first and second order derivatives of a function f(x) exit at all point in (a,b) with f'( c) =0 , where altcltb , of c and f'(x)gt0 for all points on the immediate right of c, and f'(x)lt0 for all points on the immediate left of c then at x=c , , f(x) has a

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,yinR,f(x) is differentiable and f'(0)=1. Let g(x) be a derivable function at x=0 and follows the function rule g((x+y)/(k))=(g(x)+g(y))/(k),kinR,kne0,2andg'(0)-lambdag'(0)ne0. If the graphs of y=f(x) and y=g(x) intersect in coincident points then lambda can take values

If f(x)=2 for all real numbers x, then f(x+2)=

A function g(x) is defined g(x)=2f(x^2/2)+f(6-x^2),AA x in R such f''(x)> 0, AA x in R , then m g(x) has