Let and be differentiable functions such that for every real

MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof

Problem

Let

f(x)

and

g(x)

be differentiable functions such that

f'(x)g(x)\ne f(x)g'(x)

for every real

x

. Show that between any two real solutions of

f(x)=0

, there is at least one real solution of

g(x)=0