If f(x)=3cos x, then solve the below questions:

Question

If f(x)=3cos x,

1) For what numbers x, -pi ≤ x ≤ pi, is the graph of f decreasing?

___ < x < ___

2) What is the absolute minimum value of f?

3) For what numbers, 0 ≤ x ≤ 2pi, does f(x)=0?

4) For what numbers x, -2pi ≤ x ≤ 2pi, does f(x) = 3? Where does f(x) = -3?

Answer 1

cos x and 3 cos x have the same behavior.

cos x , between 0 and pi, is decreasing

cos(pi/2) = 0, cos (3pi/2) =0

3 is the maximum value, -3 is the minimum value

Answer 2

1) cosx decreases from x = 0 to x= pi, same with 3cosx

2) absolute minimum is -3

3) pi/2 and 3pi/2 make f(x) = 0

4) f(x) = 3? means cosx = 1 and x = 0, 2pi or -2pi

f(x) =-3? means x = pi or - pi