Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let f(x) = 2x³ + 3x² - 336x. Complete this problem without a graphing calculator.
(a) The derivative of f(x) is f'(x)
= 6x^2+6x-336
(b) As a comma-separated list, the critical points of f are x =
Since f is continuous on the closed interval [−9, 15], ƒ has both an absolute maximum and an absolute minimum on the interval [-9, 15]
according to the Extreme Value Theorem. To find the extreme values, we evaluate f at the endpoints and at the critical points.
(c) As a comma-separated list, the y-values corresponding to the critical points and endpoints are y = -8,7
(d) The minimum value of f on [-9, 15] is y
the minimum value occurs at x = 7
and this x is a(n) critical point
V
-8,7
= -1519
(e) The maximum value of ƒ on [-9, 15] is y = 1856
the maximum value occurs at x = -8
and this x is a(n) end point
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Transcribed Image Text:Let f(x) = 2x³ + 3x² - 336x. Complete this problem without a graphing calculator. (a) The derivative of f(x) is f'(x) = 6x^2+6x-336 (b) As a comma-separated list, the critical points of f are x = Since f is continuous on the closed interval [−9, 15], ƒ has both an absolute maximum and an absolute minimum on the interval [-9, 15] according to the Extreme Value Theorem. To find the extreme values, we evaluate f at the endpoints and at the critical points. (c) As a comma-separated list, the y-values corresponding to the critical points and endpoints are y = -8,7 (d) The minimum value of f on [-9, 15] is y the minimum value occurs at x = 7 and this x is a(n) critical point V -8,7 = -1519 (e) The maximum value of ƒ on [-9, 15] is y = 1856 the maximum value occurs at x = -8 and this x is a(n) end point
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