Use the graph of the function to answer the following.

Question

f(x) = cos(x)

 on the interval [−2𝜋, 2𝜋]

(a) Find the x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.)

x =

(b) Find the y-intercepts of the graph of y = f(x).(Enter your answers as a comma-separated list.)

y =

(c) Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. (Enter your answers using interval notation.)

increasing:

decreasing:

(d) Find the relative extrema of the graph of y = f(x). (Enter your answers as a comma-separated list of ordered pairs.)

relative maxima:

relative minima

Answer 1

x intercepts: x = -3π/2, -π/2, π/2, 3π/2

y intercept: y = 1

increasing: (-π,0) U (π,2π)

decreasing: (-2π,-π) U (0,π)

relative maxima: (-2π,1), (0,1), (2π,1) - NOTE: Some professors/textbooks do not count endpoints on a domain as relative extrema. If endpoints are not counted, (-2π,1) and (2π,1) are not relative maxima, and your only answer is (0,1).

relative minima: (-π,-1), (π,-1)

Hope this helps!