Chapter 4, Problem 15RE

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

(a) $f\left(2\right)=4,f^{\prime }\left(2\right)=1,f^{″}\left(x\right)<0$ for $x<2,f^{″}\left(x\right)>0$ for $x>2$

(b) $f\left(2\right)=4,f^{″}\left(x\right)>0$ for $x<2,f^{″}\left(x\right)<0$ for $x>2,\underset{x\to 2^{-}}{\lim }{f}^{\prime }\left(x\right)=+\infty ,\underset{x\to 2^{+}}{\lim }{f}^{\prime }\left(x\right)=+\infty$

(c) $f\left(2\right)=4,f^{″}\left(x\right)<0$ for $x\ne 2,\underset{x\to 2^{-}}{\lim }{f}^{\prime }\left(x\right)=1,\underset{x\to 2^{+}}{\lim }{f}^{\prime }\left(x\right)=-1$