Chapter 6.4, Problem 25PPS

To determine

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

Answer to Problem 25PPS

The x coordinate of the maxima and minima are Maxima= $1.337$ and there has no minima point.

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^4{\text{+5x}}^{\text{3}}{\text{-4x}}^{\text{2}}\text{+3x-7}$ .

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:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^4{\text{+5x}}^{\text{3}}{\text{-4x}}^{\text{2}}\text{+3x-7}$ .

The graph of the given equation $\text{f}\left(\text{x}\right){\text{=-2x}}^4{\text{+5x}}^{\text{3}}{\text{-4x}}^{\text{2}}\text{+3x-7}$ by collecting the points will be:

  

Using graphing calculator,

The maxima point is $\left(1.337,-4.58\right)$ .

There has no relative minima for the given function.

Hence, the x coordinate of the maxima and minima are Maxima= $1.337$ and there has no minima point.