Is $f\left(x\right)=nx^{n}\left(1-x\right)$ uniformly convergent on $x\in\left[0,\:1\right]$

Question

Is $f_{n}\left(x\right)=nx^{n}\left(1-x\right)$ uniformly convergent on $x\in\left[0,\:1\right]$

We can see $f_{n}\left(x\right)\rightarrow f\left(x\right)=0$ point-wise, but $f_{n}\left(x\right)\geq f_{n+1}\left(x\right)$ does not seem hold ?

Answer 1

Hint You can find easily the maximum of $f_n$ (which is positive so equal to $\vert f_n\vert$) on the interval $[0,1]$ and check if $\sup_{0\le x\le 1} f_n(x)$ converges to $0$ when $n\to\infty$ or not.