Chapter 5.4, Problem 3GP

To determine

To find: the x coordinate of the relative maxima, minima and graph the function.

Answer to Problem 3GP

The relative maximum lied near $\text{x=-1}$ and that of relative minima lied near $\text{x=0}\text{.667}$ .

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=2x}}^{\text{3}}{\text{+x}}^{\text{2}}\text{-4x-2}$ .

Concept used:

Relative maxima:

Which is greater point than the points directly beside it at both sides.

Whereas,

Relative minimum:

Any point which is lesser than the points directly beside it at both sides.

Calculation:

  $\text{f}\left(\text{x}\right){\text{=2x}}^{\text{3}}{\text{+x}}^{\text{2}}\text{-4x-2}$ .

The graph of the function $\text{f}\left(\text{x}\right){\text{=2x}}^{\text{3}}{\text{+x}}^{\text{2}}\text{-4x-2}$:

  

from the graph the relative maxima and minima can be calculated as:

The coordinate $\left(-1,1\right)$ is the point which is greater than the surrounding points or the curve is open downward so there must be relative maximum near $\text{x=-1}$ .

The coordinate $\left(0.667,-3.63\right)$ is the point which is lesser than surrounding points or the curve is open upward so there must be relative minimum near $\text{x=0}\text{.667}$ .

Hence relative maximum lied near $\text{x=-1}$ and that of relative minima lied near $\text{x=0}\text{.667}$ .