Let `g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot` Then prove that `g` is increasing whenever is increasing.

phi(x)=(f(x))^(3)-3(f(x))^(2)+4f(x)+5x+3sin x+4cos x

Let h(x)=f(x)-(f(x))^(2)+(f(x))^(3) for every real number x. Then h is increasing whenever f is increasing h is increasing whenever f is decreasing h is decreasing whenever f is decreasing h is decreasing whenever f is decreasing nothing can be said in general

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

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

Prove that f(x)=x^(3) in an increasing function

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let g(x)=f(log x)+f(2-log x) and f'(x)<0AA x in(0,3) Then find the interval in which g(x) increases.

Let g(x)=3f((x)/(3))+f(3-x) and f''(x)>0 for all x in(0,3) . If "g" is decreasing in (0,alpha) and increasing in (alpha,3) ,then 8 alpha is :

Let f'(sinx)lt0andf''(sinx)gt0,AAx in (0,(pi)/(2)) and g(x)=f(sinx)+f(cosx), then find the interval in which g(x) is increasing and decreasing.

Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in