Suppose `f(x)` is a differentiable function for all x with `f'(x) le 29 and f(2) =17` . What is the maximum value of f (7) ?

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Suppose f: RvecR^+ be a differentiable function such that 3f(x+y)=f(x)f(y)AAx ,y in R with f(1)=6. Then the value of f(2) is 6 b. 9 c. 12 d. 15

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The value of f(4) is

Does there exist a differentiable function f(x) such that f(0) = -1, f(2) = 4 and f'(x) le 2 for all x. Justify your answer.

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then

Differentiate the following : f(x) = (x^(2) + 4x)^(7)

Does there exist a differentiable function f(x) such that f(0) = -1, f(2) = 4 and f'(x)le2 for all x. Justify your answer.