Extrema on a Graph: Calculus Worksheet
Explore the concepts of relative and absolute extrema of functions using graphical analysis for Grade 10 Calculus students.
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Extrema on a Graph: Calculus Worksheet
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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.