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3 cards from this section. Quick, good the night before a test.
What does the second derivative tell us about a function?
Think about how the graph curves.
If f''(x) > 0, what can you say about the graph?
Use your knowledge on what concave up looks like.
What does the second derivative indicate about a function’s concavity?
Remember the relationship between the sign of f''(x) and concavity.
True or False: Higher order derivatives can indicate points of inflection.
Think about when the concavity of a function changes.
A car's position is given by the function s(t) = t^4 - 8t^3 + 18t^2. Find the acceleration of the car and determine if the car is speeding up or slowing down at t=2.
Remember to evaluate the signs of both derivatives at t=2.
Find and classify all critical points of the function f(x) = x^4 - 4x^3. Indicate if they are local maxima, minima, or points of inflection.
Evaluate both f' and f'' around the critical points.
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