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3 cards from this section. Quick, good the night before a test.
What is the derivative of f(x) = x²?
Differentiate using the power rule.
Is f(x) = -x² increasing or decreasing?
Check the sign of the derivative.
What does it mean if f'(x) > 0?
Think about how the function behaves as its input grows.
Is local minima found where the first derivative is zero and f''(x) > 0?
Remember the role of the second derivative test.
Determine the maximum profit for a company given the profit function P(x) = -5x² + 100x, and find when it occurs.
Differentiate P(x) and set equal to zero.
A container is to be made with a square base and open top. The surface area is fixed at 100 m². Find the dimensions of the box that maximize the volume.
Express height in terms of base side length and surface area.
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