Grade 11 Calculus: Curve Sketching Worksheet
Practice worksheet for Grade 11 Calculus students focusing on curve sketching techniques including derivatives, critical points, and concavity.
Includes
Standards
Grade 11 Calculus: Curve Sketching
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Read each question carefully and show all your work. Use the provided space for your solutions. For curve sketching problems, ensure you identify critical points, intervals of increase/decrease, concavity, and inflection points.
1. Consider the function f(x) = x³ - 6x² + 5. Find the first derivative f'(x) and the second derivative f''(x).
2. For the function f(x) = x³ - 6x² + 5:
a) Determine the critical points.
b) Find the intervals where f(x) is increasing or decreasing.
3. The function f(x) is concave up when f''(x) is and concave down when f''(x) is .
4. A point where the concavity of a function changes is called an point.
5. Sketch the graph of the function f(x) = x³ - 6x² + 5. Label all critical points and inflection points, and indicate intervals of increase/decrease and concavity.
6. If f'(x) > 0 for all x in an interval, then f(x) is:
Decreasing
Increasing
Concave up
Concave down
7. A local maximum occurs where the first derivative changes from negative to positive.
True
False