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 f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f(x)=(x^(2)-2x+1)/(x+3),f i n d x: (i) f(x) gt 0 (ii) f(x) lt 0

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 f''(x) gt 0 AA x in R and let g(x)=f(x)+f(2-x) then interval of x for which g(x) is increasing is

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

If the function f (x) = {{:(3,x lt 0),(12, x gt 0):} then lim_(x to 0) f (x) =

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fog(x)=gof(x) is (a)R (b) {0} (c) {0, 2} (d) none of these

The minmumu value of the fucntion f(x)=a^2/x+b^2/(a-x),a gt 0, b gt 0 , in (0,a) is