Question

Calculus: Find the derivative.
Where does this function have horizontal tangents?
y=x^2/(x-2)

Answer 1

\[y=\frac{ x ^{2} }{ x-2 }\]

Answer 2

do u know how to get the slope of tangent to a curve ?

Answer 3

make y 0 rite? :)

Answer 4

and then find the derivative of this equation?

Answer 5

to get slope of tangent to the curve, you differentiate y to get y'
now horizontal tangent implies slope = 0 , so then put y'=0
not y=0

Answer 6

so the order is 1st find the derivative, then put y'=0

Answer 7

\[\frac{ x ^{2} -4}{ (x-2)^{2} }\]

Answer 8

thats what i got when use the quotient rule to find the derivative

Answer 9

wouldn't that be 4x ? instead of 4 ?

Answer 10

yeah sorry my cp froze on me xD

Answer 11

so now equate that to 0

Answer 12

\[\frac{ x ^{2}-4x }{ (x-2)^{2} }\]

Answer 13

ok then what :)

Answer 14

that is your y'
equate that to 0, what u get ?

Answer 15

so.. \[\frac{ x ^{2}-4x }{ (x-2)^{2} }=0\]

Answer 16

yes, which gives you ?

Answer 17

idk. :3 lol

Answer 18

when a fraction = 0, its numerator = 0

Answer 19

yeap so then what do i do with this equation

Answer 20

so u get \(x^2-4x=0\)
so which are 2 values of x, that make x^2-4x=0 ?

Answer 21

0 and 4? :D

Answer 22

that is correct

Answer 23

ok so my x values are 0,4 how do i find my y values

Answer 24

put it in y=.....

Answer 25

do i plug in my x values into the denominator to get my y values?

Answer 26

put x= 0 here
\(\large y=\frac{ x ^{2} }{ x-2 }\)
what u get ?

Answer 27

oh so in the original equation?

Answer 28

yes :)

Answer 29

so which two points did u get ?