Question

Critical values

Answer 1

deja vu

Answer 2

Similar to the last question haha

Answer 3

ahh \(99.95\%\) algebra

Answer 4

This one's a tricky one though
F(x) = x^(4/5)(x-4)^2

Answer 5

I believe I need the product rule? and the chain rule on the second part

Answer 6

no need for the chain rule here, but yes for the product rule

Answer 7

it is cooked up to work out real nice when you do the addition

Answer 8

alternatively, you could expand and get
x^(14/5)-8 x^(9/5)+16 x^(4/5) then take the derivative of that one

Answer 9

Ooh nice. Okay, lemme give it a go

Answer 10

ok have fun

Answer 11

The first way xD

Answer 12

go for it

Answer 13

Does this look right?
x^(4/5)(2x-8) + 4(x-4)^2 over 5*cuberoot(x)

Answer 14

looks right, let me check

Answer 15

Alright, and then I multiply the first fraction by 5*fifthroot(x) ?

Oh and it was supposed to be fifthroot(x), not cuberoot **

Answer 16

yeah fifth root

Answer 17

hold on a sec

Answer 18

oh yeah it is right

Answer 19

so you are going to multiply top and bottom of the first part by \(\sqrt[5]{x}\) and the roots will be gone to add, like the other one

Answer 20

What do you mean by gone to add? sorry, I'm a bit confused... why should I multiply by fifthroot(x)?

Answer 21

like the previous one, you had a sum with a denominator
you have to add to set it the numerator equal t ozero

Answer 22

If I multiply the first fraction by fifthroot(x), the denominators won't be the same though... right?

Answer 23

ok fine, multiply top and bottom by \(5\sqrt[5]{x}\)

Answer 24

\[x^{\frac{4}{5}}(2x-8)+\frac{4(x-4)^2}{5\sqrt[5]{x}}\]

Answer 25

Alright, after multiplying, I just add em up?

Answer 26

yeah in the top
still a raft of algebra

Answer 27

\[x(2x-8)+4(x-4)^2\] for the top

Answer 28

Hold up, I got 5x(2x-8) + 4(x-4)^2 for the numerator...

Answer 29

yeah you are right, i am wrong

Answer 30

Oh okay

Answer 31

So now... expand out all the terms?

Answer 32

yeah if i were you, i would cheat

Answer 33

http://www.wolframalpha.com/input/?i=5x(2x-8)+%2B+4(x-4)%5E2

Answer 34

LOL. These problems aren't graded, I'm just doing them to study. I have a quiz tomorrow :O

Answer 35

It should be pretty easy though, this is an easy unit

Answer 36

This one has been wayy longer than the ones we did in class

Answer 37

Thanks satellite :) you've been super awesome and helpful

Answer 38

yw glad it helped
you did notice you got 3 critical points right?