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

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.

Which of the following statement is always true? (a)If f(x) is increasing, then 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.

Let f(x) = x-[x] , for every real number x, where [x] is integral part of x. Then int_(-1) ^1 f(x) dx is

If f(x)=xe^(x(x−1)) , 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

Find the intervals in which the function f given by f(x) =sin x +cos x , lt=x lt=2pi is increasing or decreasing.

The function f(x) = x^(2) is decreasing in

f: RvecR ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot Then f(x) is always increasing (b) decreasing either increasing or decreasing non-monotonic

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing

If f^(prime)x=g(x)(x-a)^2,w h e r eg(a)!=0,a n dg is continuous at x=a , then f is increasing in the neighbourhood of a if g(a)>0 f is increasing in the neighbourhood of a if g(a) 0 f is decreasing in the neighbourhood of a if g(a)<0