Question

find the critical numbers of the function g(x)=x^3/4-2t^1/4

Answer 1

Is it really t^(1/4)? I'm questioning the 't'.

Answer 2

my bad it was x

Answer 3

I was looking at my book, it was originally t's but I don't like them so I change them to x

Answer 4

Not a great plan, really. Try putting tails on them and your handwriting should be more distinguishable.

Answer 5

Well, you'll need a first derivative, no?

Answer 6

right I got 3/4t^-1/4-1/2t^-3/4

Answer 7

for the first number I got t=0 if you want to go by t's

Answer 8

That's fine. Can you pretty it up a bit?

Answer 9

do you mean by factoring?

Answer 10

cause of thats what you mean you can take out a 1/4^-3/4(3t^1/2-2)

Answer 11

I don't know.

\(\dfrac{3}{4t^{1/4}} - \dfrac{2}{t^{3/4}} = \dfrac{3t^{1/2} - 8}{4t^{3/4}}\)

Kinda messy any way you look at it, but the solution is easier with only one denominator.

Answer 12

I don't understand where you got ohhhh just kidding

Answer 13

so now you have to set that equal to 0

Answer 14

I got it thank you for the help

Answer 15

How may solutions did you find?

Answer 16

2

Answer 17

t=0 and t=4/9

Answer 18

Are you sure it's not symmetric about the y-axis and there isn't another for negative t?

Answer 19

its right I looked in the back of the book

Answer 20

Books can be wrong. Good luck.

Answer 21

I'm pretty sure it's right, I mean thats what I got than checked the back