Extrema on a Graph: Calculus Worksheet
Explore the concepts of relative and absolute extrema of functions using graphical analysis for Grade 10 Calculus students.
Includes
Standards
Topics
Extrema on a Graph: Calculus Worksheet
Name:
Date:
Score:
Read each question carefully and analyze the provided graphs to determine the extrema of the functions. Provide your answers in the spaces provided.
1. Refer to the graph below. Identify all relative maxima and relative minima of the function. State the coordinates (x, y) for each point.
Relative Maxima:
Relative Minima:
2. Consider the function graphed below on the interval [-5, 5]. Identify the absolute maximum and absolute minimum values of the function.
Absolute Maximum Value:
Absolute Minimum Value:
3. A function can have more than one absolute maximum value.
True
False
4. Every continuous function on a closed interval must have an absolute maximum and an absolute minimum.
True
False
5. Which of the following statements is true about a relative extremum?
It must be an absolute extremum.
The derivative of the function at that point must be zero or undefined.
The function must be increasing on both sides of the extremum.
It can only occur at the endpoints of an interval.
6. Sketch a graph of a continuous function on the interval [-3, 3] that has a relative maximum at x=1, a relative minimum at x=-2, and an absolute maximum at x=3.
Related Worksheets
Squeeze Theorem Practice
A worksheet for Grade 10 students to practice applying the Squeeze Theorem to determine limits of functions.
Derivative by Definition Worksheet
Understand and apply the definition of the derivative to calculate derivatives of various functions.
Implicit Differentiation Worksheet
A Grade 10 Calculus worksheet on implicit differentiation, covering finding derivatives of implicitly defined functions.
Curve Sketching Mastery
This worksheet provides exercises on curve sketching, focusing on identifying key features of functions and their graphs, suitable for Grade 10 Calculus students.
First Derivative Test Worksheet
A worksheet for Grade 10 students covering the First Derivative Test, including finding critical points, intervals of increase and decrease, and local extrema.
Taylor Series Exploration
This worksheet introduces Grade 10 students to the concept of Taylor series, focusing on understanding polynomial approximations of functions.
Riemann Sums Worksheet
Explore the concept of Riemann sums to approximate the area under a curve, including left, right, and midpoint sums.
Antidifferentiation Practice
A Grade 10 Math worksheet covering fundamental concepts and techniques of antidifferentiation (integration).