Question

Problem 1: Find a non-zero function f so that f'(x) = 3f(x).

The exponential function f(x) = e^x has the property that it is its own derivative.

(d/dx) e^x = e^x

f(x) = e^(3x)

f '(x) = e^(3x) * (d/dx) 3x

= e^(3x) * 3

= 3e^(3x)

= 3 f(x)

Problem 2: Let f be your function from Problem 1. Show that if g is another function satisfying g'(x) = 3g(x), then g(x) = A f(x) for some constant A????

Answer 1