A differentiable function f(x) is defined such that, for all values of x in its domain, (i will draw the equation).

(a) what is the domain.
(b) for what values of x is f(x)=3?
(c)show that f'(x)=3^(2)f(x)
(d)solve the differential equation in (c) to find f(x) in terms of x only.

Question

A differentiable function f(x) is defined such that, for all values of x in its domain, (i will draw the equation).

(a) what is the domain.
(b) for what values of x is f(x)=3?
(c)show that f'(x)=3^(2)f(x)
(d)solve the differential equation in (c) to find f(x) in terms of x only.

anonymous · Answer

$$f(x)=3+\int\limits_{8}^{x^3}f(\sqrt[3]{t})dt$$

anonymous · Answer

$$f(x)=3\iff \int_8^{x^3}f(\sqrt[3]{t})dt=0\iff x^3=8\iff x=2$$