A differentiable function satisfies the differential equation for some constant
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
A differentiable function f satisfies the differential equation f′(x)=2cf(x) for some constant c, with initial condition f(0)=3. If (f−1)′(15)=301, what is the value of c?
(a) 2
(b) 1
(c) \dfrac{1}{900}
(d) \dfrac{\ln 5}{30}