Question

f(x)=x(4-x)^6
what are all of the critical points?

Answer 1

Have you considered the 1st Derivative?

Answer 2

Yeah that's where I'm having trouble. I used the product rule to find the derivative but idk how to find x lol

Answer 3

Demonstrate? What did the derivative look like?

Answer 4

(4-x)^6+x[-6(4-x)^5]

Answer 5

That's good. Now factor it and make it prettier. It will also be more convenient.

Answer 6

Factor or foil?

Answer 7

"FOIL" doesn't exist. Let's leave that in Algebra 1. Please FACTOR. Find common factors in each term and apply the Distributive Property.

Answer 8

okay so distribute

Answer 9

6 times..

Answer 10

No, factor.

a*b + a*c = a*(b+c)

Answer 11

ahh so (4-x)^5(4-x-6x) ???

Answer 12

That's the spirit. Now what?

Answer 13

set them both equal to 0, but for the (4-x-6x), is that [(4-x)(-6x)] or (4-7x)?

Answer 14

You have to do better than that. 4 - x - 6x = ??? You tell me. No guessing.

Answer 15

well it's equal to 0. But when i factored out the (4-x) in the beginning, there was a -6x(4-x) left. So it should really be -24x+6x^2=0 right?

Answer 16

Please simplify properly, using addition, 4 - x - 6x = ??

Answer 17

why addition?

Answer 18

Do you see anything else? Combine like terms using whatever operation is there.

Answer 19

well i was saying before that it should be multiplied right?? not added together

Answer 20

OH WAIT NVM

Answer 21

I was looking at the wrong part of it. THANK YOU SO MUCH

Answer 22

Where is the multiplication in 4 - x - 6x? You once turned it into multiplication when you wrote "[(4-x)(-6x)]". However, that was only magic. You cannot turn addition (or subtraction) into multiplication.

Answer 23

So the anwers are x=4, 4/7

Answer 24

Yea i was factoring it out weird in my head :P

Answer 25

Not quite. Those are the x-values of the critical points. You have not quite answerd the "where are" part of the question.

Answer 26

oh well I would plug those back into the original f(x) to find the y. But this is multiple choice and it just says x= lol

Answer 27

Fair enough. Good work.

Answer 28

Thank you for the help and your time! :)