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(π*0/2)*(π/2) = -sin(0)*(π/2) = 0
f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0
So this makes sense.
