Question

Use implicit differentiation to find the following:
6x^2+2y^2=42
(a) The slope of the tangent line at the indicated point on the graph
m=?
(b) The equation of the tangent line at the indicated point on the graph.
y=?

Answer 1

slope at m = 12x/4y

Answer 2

\[ \LARGE 12x+4yy'=0\quad\Rightarrow\quad y'=? \]

Answer 3

forgot - sign

Answer 4

shoot i forgot to add at point (2,-3)!!!!!

Answer 5

12*3/3*4=3

Answer 6

how about part b?

Answer 7

y+3=3(x-2)

Answer 8

so the answer is?..

Answer 9

y=3x-3

Answer 10

its saying that it is incorrect :(

Answer 11

ups sry:
y=3x-9

Answer 12

still incorrect :(

Answer 13

y=2x-7

Answer 14

thats right thank you!!
how about this one, same concept:

Answer 15

use implict differentiation to find the following:
6x^2-y^2=xy, (-1,3)
(a) The slope of the tangent line at the indicated point on the graph.
m=?
(b) The equation of the tangent line at the indicated point on the graph.
y=?

Answer 16

\[ \LARGE y'=-\frac{12x}{4y}=-\frac{3x}{y} \]
\[ \LARGE y'|_{(2,-3)}=-\frac{3\cdot 2}{-3}=2 \]
the tangent line has equation
\[ \LARGE y-y_0=y'(x_0,y_0)\cdot(x-x_0) \]
so
\[ \LARGE y-(-3)=2(x-2) \]
\[ \LARGE y=2x-7 \]

Answer 17

you should be able to do the other problem on you own!

Answer 18

thank you helder!

Answer 19

i got that m=-3 but not the y=

Answer 20

could anyone help me with that part