For the function `y=f(x)=(x^2+b x+c)e^x` , which of the following holds? `(a)`if `f(x)>0` for all real `x f'(x)>0` `(a)`if `f(x)>0` for all real `x=>f'(x)>0` `(c)` if `f'(x)>0` for all real `x=>f(x)>0` `(d)`if `f'(x)>0` for all real `x f(x)>0`

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary. For function f(x) and g(x) which of the following is true (A) f(x)g(x)gt0 for all real x (B) f(x)g(x)lt0 for all real x (C) f(x)g(x)=0 for some real x (D) f(x)g(x)=0 for all real x

If f''(x) le0 "for all" x in (a,b) then f'(x)=0

If f''(x) le0 "for all" x in (a,b) then f'(x)=0

Given that f(x)gtg(x) for all real x, and f(0)=g(0). Then f(x)ltg(x) for all x belong to

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

The curvey y=f(x) which satisfies the condition f'(x)gt0andf''(x)lt0 for all real x, is

Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>f(x+1) for all x in R (c) f(x) is invertible (d) f(x)<0 for all x in R

The curvey y=f(x) which satisfies the condition f'(x)gt0andf''(x)lt0 m for all real x, is

The f(x) is such that f(x+y) = f(x) + f(y) , for all reals x and y xx then f(0) =

If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 , find f'(5).