Mistake Master
Mistake Master · AP Calculus · Unit 3 · Step-Through Animation
Reflect the Point First, Then Flip the Slope
You'll learnhow the slope of an inverse comes straight off the mirror image, and why f′ must never be handed the number in the question.
The graph of an inverse is the original reflected across the line y = x. Reflect a tangent line and its rise and run trade places, so a slope of 3 comes back as 1/3. The hard part is not the flip but which point you flip at. Twelve short steps; press Next for each one.
f(a) = b ⇄ (f⁻¹)′(b) = 1 / f′(a) · reflect the point first
Before you start
What you're looking at
A function in blue, its inverse in pink, and the dashed mirror line y = x between them.
The question
If f climbs 3 for every 1 across at a point, what does its mirror image do, and where?