Chapter 4.1, Problem 39ES

In parts (a)-(c), sketch a continuous curve $y=f\left(x\right)$ with the stated properties.

(a) $f\left(2\right)=4,f^{\prime }\left(2\right)=0,f^{″}\left(x\right)>0$ for all $x$

(b) $f\left(2\right)=4,f^{\prime }\left(2\right)=0,f^{″}\left(x\right)<0$ for $x<2,f^{″}\left(x\right)>0$ for $x>2$

(c) $f\left(2\right)=4,f^{″}\left(x\right)<0$ for $x\ne 2$ and ${\lim }_{x\to 2^{+}}{f}^{\prime }\left(x\right)=+\infty ,{\lim }_{x\to 2^{-}}{f}^{\prime }\left(x\right)=-\infty$