Question

Graph y=sinx and y=cosx in the same viewing window. Which function could be the derivative of the other? Defend answer in terms of the behavior of the graphs.

Answer 1

The derivative of sin(x) would be cos(x).
Take a look at the window between 0 and 2pi:
At pi/2, cos(x)=0. If it were the derivative of sin(x), then that would mean it would be a local minima or maxima for the function. Since the values to the left of cos(x) are positive, and to the right of cos(x) are negative, the function sin(x) is increasing to the left of pi/2, and decreasing to the right of pi/2. Therefore, it is a local maximum.

Same argument could be applied to 3pi/2, but it is a minimum instead of the maximum.

Answer 2

d/dx sin = cosx

d/dx cos = -sinx

Answer 3

Thank you to both of you! I get it now :)