Question Number 26946 by hoangnampham13 last updated on 31/Dec/17
![f(x)=x^2 cos((1/x)) when x∈[−(1/π),(1/π)]\{0} and f(x)=0 when x=0. a) find the derivative of f(x) on the interval of [−(1/π),(1/π)]. b) compute minf(x) and maxf(x).](Q26946.png)
$${f}\left({x}\right)={x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{1}}{{x}}\right)\:{when}\:{x}\in\left[−\frac{\mathrm{1}}{\pi},\frac{\mathrm{1}}{\pi}\right]\backslash\left\{\mathrm{0}\right\} \\ $$$${and}\:{f}\left({x}\right)=\mathrm{0}\:{when}\:{x}=\mathrm{0}. \\ $$$$\left.{a}\right)\:{find}\:{the}\:{derivative}\:{of}\:{f}\left({x}\right)\:{on} \\ $$$${the}\:{interval}\:{of}\:\left[−\frac{\mathrm{1}}{\pi},\frac{\mathrm{1}}{\pi}\right]. \\ $$$$\left.{b}\right)\:{compute}\:{minf}\left({x}\right)\:{and}\:{maxf}\left({x}\right). \\ $$