Question

Find the critical numbers of the function

Answer 1

\[t^{3/4}-2t^{1/4}\]

Answer 2

\[\frac{ 3 }{ 4\sqrt[4]{t} }-\frac{ 1 }{ 2\sqrt{t^3}}\]

Answer 3

should be a 4th root on the right fraction :P

Answer 4

1/4-1=-3/4

Answer 5

ya thats on the right fraction

Answer 6

im stuck here though, should i combine them?

Answer 7

so it should be
\[ \large -\frac{1}{2\sqrt[4]{t^3}} \]

Answer 8

yes

Answer 9

go ahead. u r pretty good at this.

Answer 10

\[\frac{ 6\sqrt[4]{t^3}-4\sqrt[4]{t} }{ 8t^4 }\]

Answer 11

i suck with radicals :(

Answer 12

\[ \large y'=\frac{3}{4 t^{1/4}}-\frac{1}{2 t^{3/4}}=
\frac{3t^{1/2}-2}{4t^{3/4}} \]

Answer 13

ok?

Answer 14

wait how is the top like that?

Answer 15

\[\frac{ 2t^{1/2} }{ 8t^{3/4} }\]

Answer 16

the least common multiple of the denominators of the two fractions is 4t^{3/4}
agree?

Answer 17

yes

Answer 18

when u divide this by the denominator of the left fraction what do u get?
\[ \large \frac{4t^{3/4}}{4t^{1/4}}= \]

Answer 19

can we go back please?

Answer 20

where to?

Answer 21

am i able to cross multiply these two fractions?

Answer 22

yes. after simplification u should get what i got.

Answer 23

\[\frac{ 3^{1/1}(2t^{3/4})- 1^{1/1}(4t^{1/4}) }{ 4t^{1/4}(2t^{3/4}) }\]

Answer 24

now simplify.

Answer 25

\[\frac{ 2t^{1/2} }{ 8t }\]

Answer 26

no way.

Answer 27

watch this:
\[ \large \frac{6t^{3/4}-4t^{1/4}}{8t}=\frac{2t^{1/4}(3t^{2/4}-2)}{8t}= \]

Answer 28

now simplify

Answer 29

so i cant cross multiply?

Answer 30

yes u can. it is a little bit "unsophisticated" but after simplifing you'll get the same answer.

Answer 31

why cant i subtract the two in the numerator?

Answer 32

so we have
\[ \large y'=\frac{3t^{1/2}-2}{4t^{3/4}} \]

Answer 33

they r not like terms.

Answer 34

?? i thought 8t was in the denom?

Answer 35

did u simplify?
after simplifying this is what is left.

Answer 36

im not understanding how you are simplifying

Answer 37

\[ \large =\frac{2t^{1/4}(3t^{1/2}-2)}{8t}=
\frac{2t^{1/4}(3t^{1/2}-2)}{2\cdot4t^{1/4}t^{3/4}} \]

can u simplify now?

Answer 38

\[\frac{3}{4 t^{1/4}}-\frac{1}{2 t^{3/4}}=
\]

\[\frac{x^{1/2}}{x^{1/2}}\frac{3}{4 t^{1/4}}-\frac{2}{2}\frac{1}{2 t^{3/4}}=
\]

\[\frac{3x^{1/2}}{4 t^{3/4}}-\frac{2}{4 t^{3/4}}=\cdots
\]

Answer 39

sorry..change the x's to t's

Answer 40

ok, so i guess im following you helder,

Answer 41

now solve y'=0.

i gotta go for a while.
be right back.

Answer 42

t=4/9

Answer 43

t=0

Answer 44

t=4/9 is fine.

Answer 45

and also t=0 (the derivative doesn't exist here)