Consider the curve given by x^2 + 2x + 3y^2 = 8:

Question

(a) Find dy/dx .

(b) Find the points (x and y coordinates) where the graph of the equation has a horizontal

tangent line.

(c) Find the points (x and y coordinates) where the graph of the equation has a vertical

tangent line.

(d) Plot the curve (using plot implicit) and the tangent lines from parts (b) and (c).

Answer 1

The curve is an ellipse: [(x+1)²/9]+(y²/3)=1; you find this by completing the square.

You can compute the derivative either by implicit differentiation or solving the equation for y.

If you plot the graph, the vertical and horizontal tangents will be obvious and you can compute them from inspection of the derivative.