`h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4)` where `f''(x)> 0 AA x in (-3,4),` then `h(x)` is

If 2f(x) + 3f(-x) =15 -4x, then f(x) is equal to-

Let f(x+p)=1+{2-3f(x)+3(f(x))^2-(f(x)^3}^(1//3), for all x in R where p>0 , then prove f(x) is periodic.

Let g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot Then g(x) increases in (a) (1/2,2) (b) (4/3,2) (c) (0,2) (d) (0,4/3)

If 4f(x) + 3f(-x) = 7 - 3x, find f(x).

If 2f(x) + 3f(-x) = 15 - 4x, then prove that f(x) = 3 + 4x.

If 2f(x) - 3f(1/x) = x^2 (x ne 0) , then find f(2).

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

If f(x) = 2x^(3)-3x^(2)+ 4x - 2 , find the value of f'(-2) .

If f(x) = x^(3) - 2 px^(2) - 4 x + 5 and f' (2) = 0 find p .