Chapter 6.8, Problem 4SGR

To determine

Whether the statement “A point in the graph of a function where no other near-by point has a grater $y$ -coordinates is called a $\text{relative maximum}$ ”is true or false.

Answer to Problem 4SGR

The statement “A point in the graph of a function where no other near-by point has a grater $y$ -coordinates is called a $\text{relative maxima}$ ” is true.

Explanation of Solution

Given information:

The statement “A point in the graph of a function where no other near-by point has a grater $y$ -coordinates is called a $\text{relative maxima}$ ”

Consider the provided statement “A point in the graph of a function where no other near-by point has a grater $y$ -coordinates is called a $\text{relative maxima}$ ”

The statement is true because if looking at the graph function, A relative maxima is a point that is higher then the points directly besides it on both sides.

For example: Consider a interval $\left(-1,4\right)$ and positive value in the interval $\left(-1,4\right)$ is the equation,

By use of derivative also find the slope of a function.

Thus, the statement “The coefficient of the first terms of a polynomial in the standard form is called the $\text{leading coeficient}\text{.}$ ” is true.