Question

Given f(x) = 10- 16/x, find all c in the interval [-2,8] that satisfies the Mean Value Theorem.

Answer 1

Begin by taking the derivative ...

Answer 2

16/c^2 ?

Answer 3

Now find the slope using (-2, f(-2)) and (8, f(8))

Answer 4

i plug the -2 and 8 into the original equation for the top part correct?

Answer 5

Yes, plug both -2 and 8 into the equation.

Answer 6

For

f(8) = 10 - 16/8 = 8

Answer 7

is the slope one?

Answer 8

Where to show my work?

f(-2) = 10 + 8 = 18

Slope of (-2, 18) and (8,8) is

(18-8)/(-2 - 8) = -1

correct?

Answer 9

oh ok yeah i was adding the bottom ones

Answer 10

Set your first answer equal to -1 and solve for c ...

Answer 11

wait which one sorry

Answer 12

16/c^2 = -1

Answer 13

We have the slope of the endpoints equal to your derivative

Answer 14

got it thanks