Mistake Master
Mistake Master · AP Calculus · Unit 3 · Step-Through Animation
No y = f(x), and the Slope Still Exists
You'll learnhow to find the slope of a curve you cannot solve for y, and why every y-term hands back a dy/dx.
A circle is not a function: a vertical line hits it twice. It still has a tangent at both of those points. How do you find the slope with no y = f(x) to differentiate? Twelve short steps; press Next for each one.
every y-term is a composition · d/dx[ yⁿ ] = n yⁿ⁻¹ · dy/dx
Before you start
What you're looking at
The circle x² + y² = 25, and a vertical line about to sweep across it.
The question
If you cannot solve for y, how do you get the slope of the curve?