Question

Consider the function f(x) = 2 x^3 - 6 x^2 - 48 x + 9 on the interval [ -6 , 8 ]. Find the average or mean slope of the function on this intervalBy the Mean Value Theorem, we know there exists a c in the open interval ( -6 , 8 ) such that f'( c) is equal to this mean slope. For this problem, there are two values of c that work.

Answer 1

The mean slope is 44 i already figured it out and it is correct.

Answer 2

I need to find both values of c

Answer 3

You know how to do derivatives?

Answer 4

yes should be 6x^2 - 12x -48 right?

Answer 5

Yeup now factor this

Answer 6

set it equal to zero?

Answer 7

Yes. What do you get by setting it to zero.

Answer 8

6(x-4)(x+2) = 0

Answer 9

And your values of c are...

Answer 10

4 and -2?

Answer 11

both those are not the correct answers

Answer 12

Nope. You're not done yet.

Answer 13

plug in for y?

Answer 14

you mean for x. I think you have to do that in the original equation. I'm not sure :/

Answer 15

wouldn't i set the derivative equal to the average slope?

Answer 16

so f'x = 44

Answer 17

because its asking for 2 points c with the same slope i think

Answer 18

I think there is one value of c that equals to mean slope.

Answer 19

so 6(x-4)(x+2) = 44?

Answer 20

i get x= 5 1/3, 11 1/3 but those do not work either

Answer 21

Hmm I'm not sure anymore. I thought this was gonna work. I'll work on this.

Answer 22

so 6(x-4)(x+2) = 44?

i get x= 5 1/3, 11 1/3

Those aren't correct. Expand it all out, simplify, use quadratic formula.

Answer 23

C is 9, it is given by the function I think.

Answer 24

I think agent is right. Use the quadratic formula.

Answer 25

quadratic formula worked! -3.04, and 5.04

Answer 26

awesome!!

Answer 27

wish i could best response both of you >.<

Answer 28

I just checked your equation on wolfram alpha, and both solutions had square roots.

Answer 29

So maybe the negative one isn't right or do you think she did the quadratic equation wrong?

Answer 30

http://www.wolframalpha.com/input/?i=6+%28x-4%29+%28x%2B2%29+%3D44

Answer 31

Her answers are right. Just exact.

Answer 32

btw by "I just checked your equation on wolfram alpha, and both solutions had square roots."

i meant i checked these two: x= 5 1/3, 11 1/3

the other two were right.

Answer 33

Yeah