Chapter 6.4, Problem 24PPS

To determine

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

Answer to Problem 24PPS

There is no maxima and minima.

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^{\text{3}}{\text{+4x}}^{\text{2}}\text{-5x+8}$ .

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The graph of the function is special case of the graph of an equation.

Calculation:

The function is given as:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^{\text{3}}{\text{+4x}}^{\text{2}}\text{-5x+8}$ .

The graph of the given equation $\text{f}\left(\text{x}\right){\text{=-2x}}^{\text{3}}{\text{+4x}}^{\text{2}}\text{-5x+8}$ by collecting the points will be:

  

The given function doesn’t have a maxima and minima, meaning there are no turning points for the function. The graph clearly shows that there is no extreme function.

Hence, there is no maxima and minima.