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

If phi (x)=f(x)+f(2a-x) and f'(x) gt a, a gt 0, 0 le x le 2a , then

Let f be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x^3phi(x) for all x and y when phi (x) is a continuous function then f''(x) is equal to

Let f(x) = sin x , g (x) = x^2 and h(x) = ln x if phi(x) = h (f(g(x))) then phi^('')(x) =

"Let "f(x)=phi(x)+Psi(x) where, phi'(x) and Psi'(x) are finite and definite. Then, a. f(x) is continuous at x = a b. f(x) is differentiable at x = a c. f'(x) is continuous at x = a d. f'(x) is differentiable at x = a

Let f(x)=0 if xlt0,f(x)=x^(2) if xge0 , then for all x:

Let f(x)=x amd g(x)=|x| for all x in R . Then the function phi(x)"satisfying"{phi(x)-f(x)}^(2)+{phi(x)-g(x)}^(2) =0 is