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

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

let h(x)=f(x)-[f(x)]^(2)+[f(x)]^(3) for every real number x. Prove that h(x) is increasing or decreasing according as f(x) is increasing or decreasing.

For each of the following graphs, comment whether f(x) is increasing or decreasing or neither increasing nor decreasing at x = a.

Find the intervals in which f(x)=x^2+2x-5 is increasing or decreasing.

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Find the intervals in which the following functions are increasing or decreasing f(x)=3x^2-4x

Find the intervals in which the following functions are increasing or decreasing f(x)=6x^2-14x

Find the intervals in which the follwing functions are increasing or decreasing f(x)=5x^2+7x-13

If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

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