Let `f(x)=x^2+bx+c and g(x)=af(x)+bf\'(x)+cf\'\'(x). If f(x)gt0AAxepsilonR` then the sufficient condition of `g(x)` to be `gt0AAxepsilon R` is (A) `cgt0` (B) `bgt0` (C) `blt0` (D) `clt0`

Let g'(x)>0 and f'(x)<0AA x in R, then

Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in

Let f(x)=ax^2+bx+c,a,b,cepsilon R a !=0 such that f(x)gt0AAxepsilon R also let g(x)=f(x)+f\'(x)+f\'\'(x) . Then (A) g(x)lt0AAxepsilon R (B) g(x)gt0AAxepsilon R (C) g(x)=0 has real roots (D) g(x)=0 has non real complex roots

Let g'(x)gt 0 and f'(x) lt 0 AA x in R , then

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let f(x)=e^(x)g(x),g(0)=4 and g'(0)=2, then f'(0) equals

The function f(x)= log_(c) x , where c gt 0, x gt 0 is

Given that f(x) gt g(x) for all x in R and f(0) =g(0) then