Chapter 3.6, Problem 8CFU

To determine

To find: whether the given critical point is point of maximum, minimum, or inflection.

Answer to Problem 8CFU

Point of inflection

Explanation of Solution

Given information:

  $\begin{array}{l}y=3x^3-9x-5\\ x=-1\end{array}$

Calculation:

Put the value of x and evaluate y to create a table of values as follows:

$x$	$y$
$-$2	$-$11
$-$1	1
0	$-$5
1	$-$11
2	1

The graph for the function is as follows:

  

At the given critical point $\left(x=1\right)$ , the values decreases on going left and increases on going to right side. Hence, there is not point of maximum or minimum. This is a point of inflection.