Chapter 4.5, Problem 54E

Solution

To identify: The correct option for the statement “The graph of $y=\sec x$ never intersects the graph of $y=$ ”

Option A) $x$

Option B) $x^2$

Option C) $\csc x$

Option D) $\cos x$

Option E) $\sin x$

Option(E) is correct option for the statement “The graph of $y=\sec x$ never intersects the graph of $y=$ ”.

Given information:

The statement “The graph of $y=\sec x$ never intersects the graph of $y=$ ”

Explanation:

Consider the function $y=\sec x$ ,

The graph of $x$ is a line, so it will intersect the function.

Also, $x^2$ is a parabola, so it will also intersect the function.

The local minimum of $\cos x$ is also the local minimum of $\csc x$ .

Observe the graph of $y=\sec x$ and $y=\sin x$ .

  

They never intersect.

Thus, Option (E) is correct.