If `f(x0a n dg(x)=f(x)sqrt(1-2(f(x))^2)` are strictly increasing `AAx in R ,` then find the values of `f(x)dot`

If f(x)=4x-x^2, x in R , then write the value of f(a+1)-f(a-1)dot

f(x) is a strictly increasing function, if f'(x) is :

If f(x) = x^(3) + (a – 1) x^(2) + 2x + 1 is strictly monotonically increasing for every x in R then find the range of values of ‘a’

If f(x) is real valued function such that (f(x-1)+f(x+1))/(2f(x))=sin60^(@),AA x in R then find the value of f(x-1)+f(x+5)

If f(x) is differentiable and strictly increasing function,then the value of lim_(x rarr0)(f(x^(2))-f(x))/(f(x)-f(0)) is 1 (b) 0(c)-1 (d) 2

Show that the function f(x)=a^(x),a>1 is strictly increasing on R.

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)

Show that the function f(x) = 2x+1 is strictly increasing on R.

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x,AA x in R Then find the value of f(0)