Florida B.E.S.T. MA.912.C.2.6

MathGrades 9–12Develop an understanding for and determine derivatives.

The Standard

Find derivatives of inverse functions.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students find the derivative of an inverse function using values, formulas, graphs, or tables. They connect corresponding points and use reciprocal slopes when the original derivative is not zero.
What Mastery Looks Like: Students use a function value to match inputs between a function and its inverse. They correctly apply (f⁻¹)'(a) = 1/f'(f⁻¹(a)) and identify when the derivative is undefined.
Common Misconceptions: Students often confuse an inverse function with the reciprocal of a function. They may take the reciprocal of the derivative at the wrong input or ignore points where the original derivative is zero.
How to Assess It: Use this exit ticket: Given f(2) = 5 and f'(2) = 3, find (f⁻¹)'(5) and explain why the input is 5.

Lesson moves

Plot a function and its inverse on graph paper, draw matching tangent lines, then compare their slopes at reflected points.
Ask students to explain why finding (f⁻¹)'(5) requires locating the input where f(x) = 5.
Play a matching game with cards showing f(a), f'(a), inverse inputs, and inverse derivative values.
Use a distance-time function and its inverse to compare velocity in miles per hour with time per mile.

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