Implicit Differentitationl;finding equation

**lemontea** · June 25th 2008, 01:34 PM

Find all the points of the elispe 3x^2+2y^2=12 where the tangent line has slope 1. Make a sketch of the elispe and the tangent line to confirm your answer as well.

**Moo** · June 25th 2008, 01:52 PM

Hello,

Originally Posted by lemontea

Find all the points of the elispe 3x^2+2y^2=12 where the tangent line has slope 1. Make a sketch of the elispe and the tangent line to confirm your answer as well.

Differentiate :

$6x+2(y^2)'=0$

Using the product rule :
$(y \cdot y)'=y'y+yy'=2yy'$ .

Substituting :

$6x+4yy'=0$

We want $y'=1$

--> $6x+4y=0 \implies y=-\frac{3x}{2}$

Substituting in the equation of the ellipse :

$3x^2+2\left(-\frac{3x}2\right)^2=12$

$3x^2+\frac{9x^2}{2}=12$

$x^2+\frac{3x^2}{2}=4$

$\frac{2x^2+3x^2}{2}=4$

$5x^2=8$

$\implies x=\pm \dots$

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