Find the absolute maximum of $x^{40}-x^{20}$ on the interval $[0,1]$.

Question

Aicharya · Accepted Answer

Let $ \begin{aligned} f(x) & =x^{40}-x^{20} \ f^{\prime}(x) & =40 x^{39}-20 x^{19} \ f^{\prime}(x) & =0 \Rightarrow 20 x^{19}\left(2 x^{20}-1ight)=0 \ x & =0, x=1 \ f(0) & =0 \ f(1) & =0 \end{aligned} $ $	herefore$ Maximum value of $x^{40}-x^{20}$ in $[0,1]$ is 0

Find the absolute maximum of $x^{40}-x^{20}$ on the interval $[0,1]$.

Solution