Question

Hello,

I'm supposed to do the following questions for the equation
y=cos(pi/3)x for intervals [0,6]

a) For what values of x does the instantaneous rate of change appear to equal 0?

b) For what value(s) of x does the instantaneous rate of change appear to reach a maximum value? a minimum value?


Im guessing a) is x=3 and x=6?
I have no clue how to do b) since I know the derivative is 1/2? So not sure how to find max/min of instantaneous rate of change...

Any help is appreciated, thanks!

Answer 1

why are you guessing? I hope you actually did some kind of calculation.

since cos(kx) has period 2pi/k,
cos(pi/3 x) has period 6

the rate of change is y' = -pi/3 sin(pi/3 x)
so, it is zero at pi/3 x = 0 or pi or 2pi; that is, x = 0,3,6

sin(pi/3 x) is at a max when pi/3 x = pi/2, or x = 3/2
min at x = 5/2
Note that these values are midway between the zeros.

Don't forget your general knowledge of the shape of sine curves. Online graphing sites can help.