Solution
= Solution
\b[No.] Take the <constant function> $f(t)=c>0$, which has $f\prime=0$. The claimed inequality becomes $c^3x\le c^2x^2$, false whenever $0<x<c$.
= Solution
\b[No.] Take the <constant function> $f(t)=c>0$, which has $f\prime=0$. The claimed inequality becomes $c^3x\le c^2x^2$, false whenever $0<x<c$.