Derivatives

[tired dagger]

Can someone show me how to do this, answer is x-12y-16 but I’m not sure how.

[hoary skiff]

,rotate

[hoary skiff]

y = x⅓
y' = (1/3)x^(-2/3)
m = y'(-8) = 1/12
y = (1/12)x + c
-2 = (1/12)(-8) + c
-2 = -(2/3) + c
c = (2/3) - 2 = -4/3
y = (1/12)x - (4/3)
12y = x - 16
x - 12y - 16 = 0

@tired dagger

[tired dagger]

Sorry for late response fell asleep, could u explain how u got the 1/12 I get everything else @hoary skiff

[hoary skiff]

substitute x = -8 to y'

[tired dagger]

What do I multiply it by to get 1/12

[tired dagger]

Nevermind I got it thanks typed it wrong in calculator 😂