Chapter 4.1, Problem 48PPS

To determine

To sketch:

The graph of a function is increasing or decreasing

Explanation of Solution

Given:

The function

  $f\left(x\right)=-12x^2-14x-16$

Concept used:

Differentiating the function

  $\begin{array}{l}\frac{d^{2}V}{d{r}^2}>0\left[\text{minima}\right]\\ \frac{d^{2}V}{d{r}^2}<0\left[\text{maxima}\right]\end{array}$

Calculation:

  $f\left(x\right)=-12x^2-14x-\mathrm{16....................}\left(1\right)$

Draw the table

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

$x-axis$	$-0.66$	$0$	$-1$	$0.2$	$-1.4$
$y-axis$	$-11.91$	$-16$	$-16$	$-20$	$-18$

Draw the graph