Grade 12 Calculus: Curve Sketching
A comprehensive worksheet for Grade 12 Calculus students to practice curve sketching techniques including derivatives, critical points, concavity, and asymptotes.
Includes
Standards
Grade 12 Calculus: Curve Sketching
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Read each question carefully and provide detailed answers. Show all your work for full credit. Use the provided graph paper for sketching curves.
1. Consider the function f(x) = x³ - 6x² + 9x - 1. Find the critical points and intervals where the function is increasing or decreasing.
2. For the function f(x) = x³ - 6x² + 9x - 1, determine the intervals where the function is concave up or concave down, and find any inflection points.
3. Sketch the curve of the function f(x) = x³ - 6x² + 9x - 1 using all the information gathered from questions 1 and 2.
4. A vertical asymptote exists at x = a if the limit of the function as x approaches a from the left or right is or .
5. If f''(x) > 0 on an interval, the function is on that interval.
6. A horizontal asymptote exists if the limit of the function as x approaches infinity or negative infinity is a finite number.
True
False
7. Analyze the function g(x) = (x-1)/(x+2). Find any vertical and horizontal asymptotes. Use the graph paper to sketch the function.