Concept explainers
To Compute the values of the functions at the points indicated and Sketch its graph.
Answer to Problem 18E
The slope between the points r=0 and r=1 of the given function is 1.
Furthermore, the slope between the points r=1 and r=4 of the given function is 5.
Hence, the slope of the given function is not constant.
Explanation of Solution
Given:
The function
The given input points are as follows:
r=0
r=1
r=4
Consider the function
The given input points are as follows:
r=0
r=1
r=4
The slope between the input points r1 and r1 with output F(r1) and F(r2) , respectively is
Consider the value of function at the following points:
At r=0, we get
At r=1, we find that
At r=4, we have
Therefore, the value of the function at the points r=0, r=1, and r=4, respectively are
The slope between the points r=0 and r=1 of function (A) using formula (B) is shown below:
The slope between points r=1 and r=4 of function (A) using formula (B) is as follows:
Therefore, the slope between the points r=0 and r=1 of the given function (A) is 1.
Furthermore, the slope between the points r=1 and r=4 of the given function (A) is 5.
By determining the slopes between the points r=0 , r=1, r=4, we get different values of slopes.
Hence, the slope of the given function is not contant.
The graph of the function is shown below:
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