Mathematics

Problem

A differentiable function

f

satisfies the differential equation

f'(x)=2c\,f(x)

for some constant

c

, with initial condition

f(0)=3

. If

(f^{-1})'(15)=\dfrac{1}{30}

, what is the value of

c

? a) 2 b) 1 c) \dfrac{1}{900} d) \dfrac{\ln 5}{30}