### Home > APCALC > Chapter 6 > Lesson 6.1.4 > Problem6-47

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.) Homework Help ✎

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?

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

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