First Derivative Test Worksheet
A Grade 11 Calculus worksheet focusing on applying the First Derivative Test to find intervals of increase/decrease and local extrema.
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First Derivative Test Worksheet
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Read each question carefully and show all your work. Use the First Derivative Test to determine intervals of increase and decrease, and to classify local extrema.
1. Find the intervals on which the function f(x) = x³ - 6x² + 5 is increasing or decreasing.
2. Locate the local extrema of the function g(x) = x⁴ - 4x³ using the First Derivative Test.
3. The sign chart for the first derivative of a function h(x) is given below. Determine the intervals where h(x) is increasing or decreasing, and classify any local extrema.
4. For the function f(x) = x³ - 3x + 1, which of the following statements is true?
f(x) has a local maximum at x = 1.
f(x) has a local minimum at x = -1.
f(x) is increasing on (-∞, -1) and (1, ∞).
f(x) is decreasing on (-∞, -1).
5. If f'(x) changes from positive to negative at a critical point c, then f(c) is a .
6. If f'(x) is positive on an interval, then the function f(x) is on that interval.
7. A projectile's height (in meters) is given by h(t) = -5t² + 40t + 10, where t is time in seconds. Use the First Derivative Test to find the time at which the projectile reaches its maximum height.