Question: Define $f(x)=left{begin{array}{11}x^{2}left(2+sin frac{1}{x} ight), & text { if } x eq 0, 0, & text { if } x=0 end{array} ight. $ (a) Prove that

Define $f(x)=\left\{\begin{array}{11}x^{2}\left(2+\sin \frac{1}{x} ight), & \text { if } x eq

Define $f(x)=\left\{\begin{array}{11}x^{2}\left(2+\sin \frac{1}{x} ight), & \text { if } x eq 0, 0, & \text { if } x=0 \end{array} ight. $ (a) Prove that $f(x)$ has infinitely many critical points. (b) Prove that $x=0$ is a local minimum for $f(x)$. (c) Prove that there is no interval of the form $(0, c)$, for any $c>0$, on which $f(x)$ is increasing. CS. JG.077

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