CPM Homework Help : CALC Problem 12-37

Find 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 $y = 1$ , $x^2 – x = 6$ .

Step 2:

Therefore $x =$ ?

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 $\left(y′\right)$ from Step 3 to write the equation of the tangent line.