Optimize the following quadratic and cubic functions by (1) finding the critical value(s) at which the function
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Optimize the following quadratic and cubic functions by (1) finding the critical value(s) at which the function is optimized and (2) testing the second-order condition to distinguish between a relative maximum or minimum.
(a) y = 9x2 + 126x – 74
(1) Take the first derivative, set it equal to zero, and solve for x to find the critical value(s).
(2) Take the second derivative, evaluate it at the critical value, and check the sign for a relative maximum or minimum.
(b) y = –5x2 + 90x – 73
(c) y = x + 6x – 96x + 23
(d) y = –3x3 + 40.5x2 – 162x + 39
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ISBN: 978-1264266876
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Authors: Luis Moises Pena Levano
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