If `f(x)` is twice differentiable and continuous function in `x in [a,b]` also `f'(x) gt 0` and `f ''(x) lt 0` and c in (a,b) then `(f(c) - f(a))/(f(b) - f(a))` is greater than

If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

If f(c) lt 0 and f'(c) gt 0 , then at x = c , f (x) is -

f(x) is a continuous and differentiable function. f'(x) ne 0 and |{:(f'(x),f(x)),(f''(x),f'(x)):}|=0 . If f(0)=1 and f'(0)=2 then f(x)=....

Let f be a differentiable real function defined on (a;b) and if f'(x)>0 for all x in(a;b) then f is increasing on (a;b) and if f'(x)<0 for all x in(a;b) then f(x) is decreasing on (a;b)

Let f be any continuously differentiable function on [a,b] and twice differentiable on (a,b) such that f(a)=f'(a)=0 . Then

Let f be any continuously differentiable function on [a, b] and twice differentiable on (a, b) such that f(a)=f'(a)=0" and "f(b)=0 . Then-