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

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)

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

Let phi(a)=f(x)+f(2ax) and f'(x)>0 for all x in[0,a]. Then ,phi(x)

Let f(x) be a quadratic expression possible for all real x. If g(x)=f(x)-f'(x)+f''(x), then for any real x

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

Let f(x)=x^(2)+4x+1. Then (A) f(x)>0 for all x(B)f(x)>1 when x>=0 (C) f(x)>=1 when x<=-4(D)f(x)=f(-x) for all x

Let f(x+y)=f(x)+f(y)+2xy-1 for all real x and f(x) be a differentiable function.If f'(0)=cosalpha, the prove that f(x)>0AA x in R