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.

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

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

Prove that f(x)=x-sinx is an increasing function.

Let g(x)=f(logx)+f(2-logx)a n df^(x)<0AAx in (0,3)dot Then find the interval in which g(x) increases.

Let g(x)=f(x)+f(1-x) and f "(x)>0AAx in (0,1)dot Find the intervals of increase and decrease of g(x)dot

If f(x)=sinx+cosx and g(x)=x^2-1 , then g(f (x)) is invertible in the domain .

If f(x)=sinx+cosx and g(x)=x^2-1 , then g(f (x)) is invertible in the domain .

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is a. increasing in (0,3a) decreasing in (3a, 4a) b. increasing in (a, 4a) decreasing in (5a ,oo) c. increasing in (0,4a) d. none of these

If f(x)=(x^2)/(2-2cosx);g(x)=(x^2)/(6x-6sinx) where 0 < x < 1, then (A) both 'f' and 'g' are increasing functions