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Handout Friday 10/31
Let’s practice using the first and second derivative tests to explore the behavior of some functions, including finding local maxima and minima, intervals on which the function is increasing or decreasing, inflection points, and any asymptotes.
Start with an easier one: \(f(x) = x^3 - 3x + 2\text{.}\)
Next, try a slightly more complicated example: \(f(x) = \dfrac{x^2}{x^2 - 2x + 1}\text{.}\) Note we need to use the quotient rule here, and then factor the numerator to simplify it.
Another similar one: \(f(x) = \dfrac{x^2+4}{x}\text{.}\)
