CPM Homework Help : APCALC Problem 12-34

Write the equation of the line tangent to the curve $x^{2}y - xy^{2} = 6$ at the point in the first quadrant where $y = 1$ .

Step 1:

When $y = 1$ , $x^{2} - x = 6$ .
Therefore $x =$ ?

Step 2:

$2xy+x^2y^\prime-y^2-x(2y)y^\prime = 6$

Step 3:

Substitute the values of the coordinates of the point into the equation in Step 2. Then solve for $y′$ .

Step 4:

Use the point from Step 1 and the slope ( $y′$ ) from Step 3 to write the equation of the tangent line.