f(x)=2f((x^(2))/(2))+f(6-x^(2))AA x in R

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 mg(x) has

Discuss the monotonocity of Q(x), where Q(x)=2f((x^(2))/(2))+f(6-x^(2))AA x in R It is given that f'(x)>0AA x in R. Find also the point of maxima and minima of Q(x)

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

Suppose f'(x) exists for each x and h(x)=f(x)-(f(x))^(2)+(f(x))^(3) AA x in R , then

Suppose f'(x) exists for each x and h(x)=f(x)-(f(x))^(2)+(f(x))^(3) AA x in R , then

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

f(x^(2)+x)+2f(x^(2)-3x+2)=9x^(2)-15x AA x in R find f(2016) Find f:R rarr R ,such that f(x)+xf(1-x)=1+x AA x in R

If g(x)=2f(2x^(3)-3x^(2))+f(6x^(2)-4x^(3)-3)AA x in R and f'(x)>0AA x in R then g(x) is increasing in the interval

f:R rarr R is given by f(x)=(a^(x))/(a^(x)+sqrt(a))AA x in R , then f((1)/(40))+f((2)/(40))+......+f((39)/(40))-f((1)/(2))=

If f (x) +2 f (1-x)( =x ^(2) +2AA x in R and f (x) is a differentiable function, then the vlaue of f'(8) is