Q. 36 - Calculus

Question

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

$f\left(x\right)=sex x$

Step-by-Step Solution

Answer

The critical points is $x=0$. The graph of the function is shown below .

Step 1. Given information

Consider the given function $f\left(x\right)=sec x$ .

Step 2. Find the critical points .

To find the critical points differentiate the given function .

$$\begin{gathered} f\left(x\right)= sec x \\ f\text{'}\left(x\right)= sec x·\tan x \end{gathered}$$

$sec x$not equal to zero since that would mean $\cos x =\frac{1}{0}$= undefined so $\tan x =0$.

Therefore the critical point is $x=0$ .

Step 3. Plot the graph .

The graph of the given function by using graphing utility is shown below.

From the given graph function f has both local maximum and local minimum because the turning points are on both axis .