Extrema in Calculus Worksheet
A Grade 12 Calculus worksheet focusing on finding and classifying extrema of functions using derivatives.
Includes
Standards
Topics
Extrema in Calculus
Name:
Date:
Score:
Read each question carefully and show all your work. Use calculus techniques to find and classify extrema.
1. Find all critical points and classify them as local maxima, local minima, or neither for the function f(x) = x³ - 6x² + 5.
2. What are the absolute maximum and minimum values of the function g(x) = x² - 4x + 1 on the interval [0, 3]?
Max: 1, Min: -3
Max: 1, Min: -2
Max: 3, Min: -2
Max: 3, Min: -3
3. If f'(x) changes from positive to negative at x = c, then f has a local at x = c.
4. If f'(x) changes from negative to positive at x = c, then f has a local at x = c.
5. Use the Second Derivative Test to classify the critical points of f(x) = x⁴ - 8x².
6. A function can have an absolute maximum or minimum at a point where its derivative is undefined.
True
False
7. A rectangular box with a square base and no top is to be made from 1200 cm² of material. Find the dimensions of the box that will maximize its volume.
Related Worksheets
Limits at Infinity Worksheet
This worksheet focuses on evaluating limits of functions as the variable approaches infinity, covering various techniques and function types relevant to Grade 12 Calculus.
Quotient Rule Practice Worksheet
A Grade 12 Calculus worksheet focusing on applying the quotient rule for differentiation.
Grade 12 Calculus: Related Rates Worksheet
A Grade 12 Calculus worksheet covering related rates problems, including applications in geometry and physics.
Taylor Series Exploration
A Grade 12 Calculus worksheet exploring Taylor series, focusing on definition, expansion, and common applications.
Particle Motion Calculus Worksheet
A Grade 12 Calculus worksheet focusing on particle motion, including displacement, velocity, acceleration, and interpreting motion graphs.
Lagrange Error Bound Worksheet
A Grade 12 Calculus worksheet focusing on understanding and applying the Lagrange Error Bound for Taylor polynomials.
U-Substitution Calculus Worksheet
A Grade 12 Calculus worksheet focusing on integration using the u-substitution method with various problem types.
Derivative Graphs Analysis
Analyze and interpret the graphs of functions and their derivatives, identifying key features such as increasing/decreasing intervals, local extrema, concavity, and points of inflection.