Question

Let f be a differentiable function with selected values given in the table above. What is the average rate of change of f over the closed intervals 0<_ x <_10?

Answer 1

B

Explanation:

Answer 2

B

Explanation:

The average rate of change is synonymous with the slope.

So, essentially, we want to find the average slope of our function f(x) from x=0 to x=10.

So, we will use the two following points: (0,5) and (10, -20).

Recall the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Let (0, 5) be (x₁, y₁) and (10, -20) be (x₂, y₂). Substitute. This yields:

`m=(-20-5)/(10-0)`

Subtract and reduce:

`m=-25/10=-5/2`

So, the average slope of f(x) between x=0 and x=10 is -5/2.

Our answer is B.

And we're done!