Answer: The derivate is f'(x) = -sin(πx/2)(π/2)
Step-by-step explanation:
We want the value of the derivate at each point marked:
As you may know, the derivate of cos(x) is equal to -sin(x)
And in our case:
f(x) = cos(πx/2)
f'(x) = -sin(πx/2)(π/2)
Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))g'(x)
Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:
f'(0) = -sin(π0/2)(π/2) = -sin(0)(π/2) = 0
f'(2) = -sin(π2/2)(π/2) = -sin(π)*(π/2) = 0
So this makes sense.
