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Calculus · DER
Optimization — Find Absolute and Local Extrema
Closed-interval method: evaluate f at all critical numbers and endpoints; largest is the max, smallest is the min.
CalculusCommon Core FUN-1.DDERVerified correct ✓
Worked examples
A company's profit function is P(x) = −2x² + 97x − 41, where x is the number of units produced (in hundreds). (a) Find the critical number(s) by setting P'(x) = 0. (b) Use the second derivative test to classify each critical point as a local maximum, local minimum, or saddle point. (c) State the absolute maximum profit on the interval [0, 97].
Answer:
A company's profit function is P(x) = −2x² + 55x − 80, where x is the number of units produced (in hundreds). (a) Find the critical number(s) by setting P'(x) = 0. (b) Use the second derivative test to classify each critical point as a local maximum, local minimum, or saddle point. (c) State the absolute maximum profit on the interval [0, 55].
Answer:
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