First Derivative Test Worksheet
A Grade 11 Calculus worksheet focusing on applying the First Derivative Test to find intervals of increase/decrease and local extrema.
Includes
Standards
Topics
First Derivative Test Worksheet
Name:
Date:
Score:
Read each question carefully and show all your work. Use the First Derivative Test to determine intervals of increase and decrease, and to classify local extrema.
1. Find the intervals on which the function f(x) = x³ - 6x² + 5 is increasing or decreasing.
2. Locate the local extrema of the function g(x) = x⁴ - 4x³ using the First Derivative Test.
3. The sign chart for the first derivative of a function h(x) is given below. Determine the intervals where h(x) is increasing or decreasing, and classify any local extrema.
4. For the function f(x) = x³ - 3x + 1, which of the following statements is true?
f(x) has a local maximum at x = 1.
f(x) has a local minimum at x = -1.
f(x) is increasing on (-∞, -1) and (1, ∞).
f(x) is decreasing on (-∞, -1).
5. If f'(x) changes from positive to negative at a critical point c, then f(c) is a .
6. If f'(x) is positive on an interval, then the function f(x) is on that interval.
7. A projectile's height (in meters) is given by h(t) = -5t² + 40t + 10, where t is time in seconds. Use the First Derivative Test to find the time at which the projectile reaches its maximum height.
Related Worksheets
Introduction to Differential Equations
This worksheet introduces fundamental concepts and methods for solving basic differential equations suitable for Grade 11 students.
Extrema in Calculus
Explore finding local and absolute extrema of functions using derivatives in this Grade 11 Calculus worksheet.
Squeeze Theorem Worksheet
A Grade 11 Math worksheet focusing on understanding and applying the Squeeze Theorem to evaluate limits, with various question types.
AP Calculus Foundations Worksheet
This worksheet covers fundamental concepts in AP Calculus, including limits, derivatives, and their applications, suitable for Grade 11 students.
Limits and Continuity Worksheet
Grade 11 Calculus worksheet covering limits, continuity, and related concepts with various question types.
Limits at Infinity Worksheet
Explore the behavior of functions as input values approach positive and negative infinity with this Grade 11 Calculus worksheet.
Intermediate Value Theorem Worksheet
Explore the Intermediate Value Theorem with this worksheet for Grade 11 Calculus students, covering its definition, application, and conditions.
Product Rule Practice Worksheet
Practice applying the product rule for differentiation in various calculus problems.