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4 cards from this section. Quick, good the night before a test.
Find the first derivative of the function f(x) = 3x² - 5x + 2.
Differentiate each term of the polynomial.
Identify a critical point for the function f(x) = x² + 4.
Calculate the derivative and check for zeros.
What is a critical point?
Focus on the definition of critical points.
True or False: A critical point can be a minimum even if it doesn't satisfy f'(x) = 0.
Consider cases where the derivative might not be defined.
A company models its profit as P(x) = -x³ + 9x² - 24x. Find the critical points and classify them.
Use the first derivative test for classification.
Find the local extrema for the function f(x) = x⁴ - 4x³ + 4x. Determine not only the points but also the function's behavior.
Graphing the function could provide visual insight into its behavior.
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