Chapter 3.6, Problem 11CFU

To determine

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

Answer to Problem 11CFU

Minimum point

Explanation of Solution

Given information:

  $\begin{array}{l}y=x^6-3x^4+3x^2-1\\ x=0\end{array}$

Calculation:

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

$x$	$y$
$-$2	27
$-$1	0
0	$-$1
1	0
2	27

The graph for the function is as follows:

  

At the given critical point, 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.

At $x=0$ , the graph is decreasing on the left and increasing on the right. The value of relative minimum is $\left(0,0\right)$ . Thus, the critical point is a minimum point of the function.