CPM Homework Help : CALC3RD Problem 6-47

Sketch a graph of $x^2 + y^2 = 4$ . Predict the slopes of the tangent lines at $x = 0$ . Then, confirm this algebraically by differentiating. (Hint: Solve for $y$ first.)

Hint:

Sketch the graph (it's a circle). Then sketch the tangents (they are horizontal). What do you predict the slope of the tangents to be?

Hint:

Confirm your prediction by evaluating the derivative of the circle at $x = 0$ .

Note: Before differentiating, solve for $y: \ y=\pm \sqrt{4-x^{2}}$ .