Question

Use the graph of f(x) below to estimate the value of f ′(0):

Graph is an inverted parabola with x intercepts at x equals negative 3 and positive 3 and y intercept at y equals 9.

9
0
1
f ′(0) is undefined

Answer 1

that's the slope at x=0
seems to be a horiztontal line
so the slope is 0

answer is 2nd one

Answer 2

Option B.

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.