Answer:
Option B.
Step-by-step explanation:
The given graph is an inverted parabola with x intercepts at x = - 3 and x = 3
and y- intercept at y = 9.
Vertex form of this parabola is represented by y = -(x - h)² + k
where (h, k) are the coordinates of the vertex of this parabola.
Vertex of the given parabola is (0, 9).
So the equation of the parabola will be y = -(x - 0)² + 9
y = -x² + 9
In the function form : f(x) = -x² + 9
Now we can find the derivative of the function as
f'(x) = -2x + 0 [Since derivative of a constant is always 0]
f'(x) = -2x
f'(0) = -2(0)
Therefore, option B. is the answer.
