Question

Given f(x) = 3 - sin(πx/3)

a. sketch the graph of f(x)
b. find the period of f(x).
c. compute the max value of f(x)
d. what is the smallest positive x for which f(x) is a maximum?

Answer 1

See explanation

Explanation:

A. The graph of the function
`f(x)=3-\sin (\pi x)/(3)` is shown in attached diagram.

B. The period of the function
`f(x)=3-\sin (\pi x)/(3)` is

`T=(2\pi)/((\pi)/(3))=6.`

C. The values of
`\sin (\pi x)/(3)` are
`[-1,1],` so the maximum value of the function
`f(x)=3-\sin (\pi x)/(3)` is

`3-(-1)=4.`

D. The smallest positive x for which f(x) is maximum is x=4.5 (black point on the graph).