Suppose that `f(0)=-3` and `f'(x)<=5` for all real values of `x`. Then the largest value of `f(2)` can attain is

Let f:RtoR be such that f(1)=3 and f'(1)=6 . Then lim_(xto0)[(f(1+x))/(f(1))]^(1//x) equals

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

Suppose that f(x) is continuous in [0, 1] and f(0) = 0, f(1) = 0 . Prove f(c) = 1 - 2c^(2) for some c in (0, 1)

Let f is a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx, f(0) = (4-e^(2))/(3) , find f(x).

Choose the correct answer If d/(dx)f(x)=4x^(3)-3/(x^(4)) such that f (2) = 0. Then f (x) is

Find the derivative of the function f(x)=2x^(2)+3x-5" at "x=-1 . Also prove that f'(0)+3f'(-1)=0 .

Find the derivative of the function f(x)= 2x^(2)+3x-5 at x=-1 .Also prove that f'(0)+3f'(-1)=0

Let the function f: [-7,9] to R be continuous on [-7,0] and differential on (-7,0) . If f(-7) =-3 and f'(x) le 2 , for all x in (-7,0) , then for all such function f,f(-1)+ f(0) lies in the interval :

f(x+y) = f(x) + f(y), "for " AA x and y and f(x)= (2x^(2) + 3x) g(x) . For AA x . If g(x) is a continuous function and g(0)= 3 then f'(x) = ……….