Let be twice differentiable function such that for a differentiable function

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Let

f:(a, b) \rightarrow R

be twice differentiable function such that

f(x)=\int_a^x g(t)\,dt

for a differentiable function

g(x)

. If

f(x)=0

has exactly five distinct roots in

(a, b)

, then

g(x)g'(x)=0

has at least: (a) twelve roots in

(a, b)

(b) five roots in

(a, b)

(a, b)

(d) three roots in

(a, b)