Derivative Explanation Help

Question

Basically, I am trying to prove that number 15 relates to the graph of D, but I was wondering if my explanation was correct. Here is the problem and here is what I wrote. Also, I was wondering if there was a more efficient way of writing this, since I am repeating a lot and the graph doesn't have points on the axis.

Problem: https://i.stack.imgur.com/GYXQN.png

Explanation: From the first interval, the function is increasing, so f ' > 0. From the next interval, the function is decreasing. so so f ' < 0. From the third interval, the function is increasing, so f ' > 0. From the fourth interval, the function is decreasing, so f ' < 0. From the last interval, the function is increasing, so f ' > 0. The graph the corresponds to this is D, because from the first interval, f ' is above zero on the y - axis, from the second interval, f ' is below zero on the y - axis, from the third interval, f ' is below above zero on the y - axis, from the fourth interval, f ' is below zero on the y - axis, and from the fifth interval, f ' is above zero on the y - axis.

Answer 1

I think all the question is wanting is that taking the derivative of f(x), which is cos(x), becomes -sin(x).

Also, a derivative phase shifts f(x) left by π/2.