Dawson Rowe
04/27/2024 · High School
efine Critical Point. Determine the interval over which \( f \) is i) increasing ii) decreasing i) neither increasing nor decreasing iv) concave up v) concave down. If \[ f(x)=\frac{2 x^{3}}{3}-5 x^{2}-\frac{1}{x}-3 \]
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1. Find the critical points by solving \( f'(x) = 0 \).
2. Determine the intervals of increase and decrease by testing points around the critical points.
3. Find the concavity by solving \( f''(x) = 0 \) and testing points around the inflection points.
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