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3 cards from this section. Quick, good the night before a test.
What is a critical point?
Think about where the slope of the tangent is horizontal.
What indicates a local maximum?
Remember the concept of rising and falling?
What do we call a point where a function reaches its highest value locally?
Think of a hilltop versus a valley.
At a critical point, the first derivative of a function is:
It indicates changes in direction.
Given the function f(x) = x^4 - 8x^3 + 18x^2, find its local maxima and minima.
Check changes in signs from f' around critical points.
A farmer wants to create a rectangular pen using one side of a barn as an enclosure. If the total length of fencing available is 30m, what length and width will maximize the area?
Formulate the area equation and differentiate to find critical points.
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