Question

Slope of the curve y^3-xy^2=4 at point where y=2 is ____

Answer 1

what our implicit derivative?

Answer 2

y^3-y^2=0?

Answer 3

hmm, not quite

y^3 power rule it: 3y^2 y'

-xy^2 is a product so .. -x'y^2 -2xy y'

and 4 is a constant so it goes to 0

Answer 4

solve for y', and you need to solve for x as well, then all the parts are there to plug in

Answer 5

ok gimme a sec

Answer 6

3y^2+2x'y^3y'=0

Answer 7

y'=-3/2x'y

Answer 8

y^3 - xy^2 = 4

3y^2 y' -x'y^2 - 2xy y' = 0




let y=2

2^3 - x 2^2 = 4

3 2^2 y' -2^2 - 2x 2 y' = 0
------

8 - 4x = 4 , x=1

12y' -4 - 4y' = 0 , now all we need is to solve for y'

Answer 9

most times its simpler to just solve for y' after all the other parts are in place

Answer 10

i think i understand

Answer 11

thank you

Answer 12

good luck

Answer 13

but wait

Answer 14

what happened to the x'

Answer 15

x', with respect to x is just: dx/dx which is equal to 1

Answer 16

ok

Answer 17

what is the rate of change of x as x moves by 1? well, 1 of course :)

Answer 18

now if we had x as a function of time, then dx/dt would have to have been given to us or left alone as x'

Answer 19

i think that is one of the later problems on my sheet

Answer 20

y'=-1/2

Answer 21

thank you a TON!

Answer 22

12y' -4 - 4y' = 0

12y' - 4y' = 4

8y' = 4 , im getting +1/2

Answer 23

oh whoops forgot the negative

Answer 24

wow that was bad

Answer 25

:)

Answer 26

:)