Statement 1: `f(x)=x+cosx` is increasing `AAx in Rdot` Statement 2: If `f(x)` is increasing, then `f^(prime)(x)` may vanish at some finite number of points.

Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even function.

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

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

Statement - I : If f(x) = sinx, then f'(0) = f'(2pi) Statement - II : If f(x) = sin x , then f(0) =f(2pi) .

The function f(x)= 4x^2+2x+1 is increasing for?

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.

The function f(x)=(sinx+cosx) is an increasing function in

Statement - I : If f(x) is an odd function, then f'(x) is an even function. Statement - II : If f'(x) is an even function, then f(x) is an odd function.

Statement 1: If f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)), then f(x) is positive for all x in R_0dot Statement 2: f(x) is increasing for x >0 and decreasing for x<0

Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing for every x in (-oo,1)uu(2,3) Statement 2: f(x) is increasing for x in (1,2)uu(3,oo) and has no point of inflection.