Chapter 1.3, Problem 40E

Solution

(a)

To find: The interval for which function is increasing or decreasing

Function is increasing and decreasing on a fixed interval. Function is decreasing on (-6.3,-3.3) and increasing on (-3.3,0]. Further it decreasing on (0,3.3) and start increasing on (3.3,6.3)

Given information:

The function is $g(x)=4\cos x$

The graph of the function is given below:

  

It can be observed from the graph that function is decreasing on (-6.3,-3.3) and increasing on (-3.3,0].further it decreasing on (0,3.3) and start increasing on (3.3,6.3).It is observed that function is increasing and decreasing on a fixed interval.

(b)

To find: The function is even.

Function is even

Given information:

The function is $g(x)=4\cos x$

  $\begin{array}{l}g\left(-x\right)=4\cos \left(-x\right)\\ g\left(-x\right)=4\cos x=f\left(x\right)\end{array}$

The function is even.

(C)

To find: The extrema of the function .

The extrema of the function is at point A and B

Given information:

The function is $g(x)=4\cos x$

The function has local minima at point B and local maxima at point A.

(d)

To find: The graph related to the 12 basic functions.

Function is related to basic cosine function.

Given information:

The function is $g(x)=4\cos x$

Function is related to basic cosine function.