# Question #b1bc4

Jul 22, 2017

#### Answer:

I believe that there is no such function.

#### Explanation:

${\lim}_{x \rightarrow - {5}^{-}} f \left(x\right) = \infty$ and

$f ' \left(x\right) < 0$ on $\left(- \infty , 1\right)$ are not both possible.

A function can not approach infinity by decreasing.

If ${\lim}_{x \rightarrow - {5}^{-}} f \left(x\right) = - \infty$, then we have a problem with concavity.

The condition $f ' ' \left(x\right) > 0$ on $\left(- \infty , - 3\right)$ requires $f$ to be concave up left of $x = - 3$.