If `f^(2)(x)+f(x)=g(x)` and `g(x)` is always increasing then the minimum value that `f(x)` can attain so that `f(x)` also increasing is 'k'? Then `(2(k+1))` is

If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is

If f(x)=x^(2)g (x) and g(1)=6, g'(x) 3 , find the value of f' (1).

The minimum value attained by f(x) ,where f(x)=(x^(2)-4x+6) ,is

If f(x) and g(x) are two positive and increasing functions,then which of the following is not always true? [f(x)]^(g(x)) is always increasing [f(x)]^(g(x)) is decreasing, when f(x) 1. If f(x)>1, then [f(x)]^(g(x)) is increasing.

If f(x0 and g(x)=f(x)sqrt(1-2(f(x))^(2)) are strictly increasing AA x in R, then find the values of f(x)

If f(x)=2x+tan x and g(x) is the inverse of f(x) then value of g'((pi)/(2)+1) is

Let g(x) = 2 f(x/2)+ f(2-x) and f''(x) lt 0 forall x in (0,2) . Then calculate the interval in which g(x) is increasing.

Statement 1: The function f(x)=x In x is increasing in ((1)/(e),oo) Statement 2: If both f(x) and g(x) are increasing in (a,b), then f(x)g(x) must be increasing in (a,b).

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.