Question

Help: See attachment

Answer 1

Oh isn't that related to the Mean Value Theorem?

Answer 2

I don't know I am really confused on what to do

Answer 3

First thing you want to do is find what exactly that rate of change is between the two points.

Answer 4

ok

Answer 5

At x=4, the function returns 0. At x=9, the function returns 35. What would you say is the rate of change between the two?

Answer 6

it would be 5

Answer 7

The x changes by 5 yes, but how much does the y value change by in that frame?

Answer 8

35

Answer 9

Yep, so for every 1 x, how much does y change?

Answer 10

5

Answer 11

Check again, y needs to get to 35 in the same time x needs to get from 4 to 9, which is just 5 difference. Divide 35 by 5 to find how much 1 x changes y by.

Answer 12

7

Answer 13

Yep, so now that we know the average slope (7), we can begin to find the point where the function has that slope.

Answer 14

First you want to take the derivative of the function, which would be:

f'(x)=2x-6

Answer 15

ok

Answer 16

The derivative is just another way of saying "slope at a given x". Since the derivative is really just the slope, let's solve for what x has to be to make the derivative equal to 7:

7=2x-6
13=2x
x=6.5

Answer 17

So this means at x=6.5, the slope is equal to the average slope of that whole line segment.

Answer 18

Does that all make sense?

Answer 19

ok

Answer 20

so then is that the final answer or is there more

Answer 21

Yep, that's the final answer. We just needed to find the x value that produces the point with the same slope as the average slope from x=4 to x=9.

Answer 22

ok got it I think I was making it hARDER THAN IT WAS THANKS FOR ALL YOUR HELP

Answer 23

Yeah no problem, math is confusing when teachers teach it, so I like to teach it using human vocabulary ^^

Answer 24

yup it works better that way thansk and you are a great teacher