Exercise · ZW-CRITICAL-POINTS-003 · ★★☆ Intermediate
What are the critical points of \(f(x)=2 x^{3} - 9 x^{2} + 12 x\)?
Choose one option.
Show answer
- B. \(x=1,\ x=2\)
Explanation
Differentiate: \(f'(x)=6 x^{2} - 18 x + 12=6 \left(x - 2\right) \left(x - 1\right)\). The critical points are the solutions of \(f'(x)=0\): \(x=1,\ x=2\).
Review the concept: Critical points
A critical point of \(f\) is a number \(c\) in the domain where \(f^{\prime}(c)=0\) or \(f^{\prime}(c)\) does not exist. Local maxima and minima of a function at an interior point occur at critical points.
\[f'(c)=0\ \ \text{or}\ \ f'(c)\ \text{does not exist}\]
More practice problems: critical points
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