Derivative of Inverse Functions
Authored by Christie Page McAlum
Mathematics
11th Grade - University
CCSS covered
Used 95+ times
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About
This quiz focuses on the derivatives of inverse functions, a fundamental topic in differential calculus typically covered in Advanced Placement Calculus AB/BC or college-level Calculus I courses. The material is appropriate for grade 11 students in advanced mathematics tracks or university freshmen. Students must understand the relationship between a function and its inverse, specifically that if H(x) = f⁻¹(x), then H'(x) = 1/f'(f⁻¹(x)). The core concept being assessed is the inverse function derivative rule, which states that the derivative of an inverse function at a point equals the reciprocal of the derivative of the original function at the corresponding point. Students need solid foundational knowledge of function notation, inverse functions, the chain rule, and the ability to apply the formula for finding derivatives of inverse functions in various contexts. Created by Christie Page McAlum, a Mathematics teacher in the US who teaches grade 11 and University level courses. This quiz serves as an excellent tool for formative assessment after introducing the derivative of inverse functions theorem, allowing students to practice applying the fundamental relationship between derivatives of inverse functions. Teachers can use this as a warm-up activity to check understanding before moving to more complex applications, as homework to reinforce the day's lesson, or as a quick review before a unit test on advanced differentiation techniques. The quiz aligns with Common Core State Standards for Mathematics A-REI.D.11 and F-BF.B.4, as well as College Board AP Calculus standards focusing on derivatives of inverse functions and their applications in solving real-world problems.
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9 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If H(x) = f -1(x), then H'(3) equals
4
1/4
- 1/4
-4
Tags
CCSS.HSF-BF.B.4A
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the derivative of the inverse
Tags
CCSS.HSF-BF.B.4A
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Find h'(3)
Tags
CCSS.HSF.IF.A.1
CCSS.HSF.IF.A.2
CCSS.HSF.IF.B.4
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Tags
CCSS.HSF-BF.B.4A
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Tags
CCSS.HSF-BF.B.4A
6.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Tags
CCSS.HSF-BF.B.4A
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Tags
CCSS.HSF-BF.B.4A
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