Question

find the tangents of the curve xy=18 from (4,4) please help. the answers are x+ 2y = 12 and 2x + y = 12

Answer 1

@phi

Answer 2

did you find dy/dx ?

Answer 3

im not sure.. its x?

Answer 4

its 1

Answer 5

\[ y = 18 x^{-1} \]
what is dy/dx?

Answer 6

-18/ x^2

Answer 7

that will be the slope of the tangent line at (x,y) on the curve
the slope will also be (y-4)/(x-4)
so we have an equation

Answer 8

okay okay

Answer 9

i got x^2 - 4x^2 + 18x + 72

Answer 10

x^2y - 4x^2 + 18x + 72

Answer 11

is that = 0 ?

double check your sign on 72

Answer 12

yes it is. - 72

Answer 13

x^2y - 4x^2 + 18x - 72 =0

use y = 18/x to replace the y
simplify and factor to find the roots

Answer 14

thanks @phi :))