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.
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!
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