F(x)= (−2x^3) + (3.72x^2)+123.552x +64.2 ... Find Local Max?

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f(x)= (−2x^3) + (3.72x^2) + 123.552x + 64.2

FIND EXACT ANSWER. DO NOT PUT IN DECIMAL FORM

a) is increasing on the interval ( , )

b) It is decreasing on the interval (-inf , ) and the interval ( ,inf)

c) Local max = ?

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1 Answer

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  • Aaron
    Lv 5
    10 years ago
    Favorite Answer

    Find the first derivative to get the local min and max.

    f '(x) = -6x^2 + 7.44x + 123.552

    Setting this equal to 0 and solving gives us two solutions: 5.2 and -3.96

    (a) So, it must be increasing on (-3.96, 5.2).

    (b) It must be decreasing on (-inf, -3.96) and (5.2, inf)

    (c) The local max is at x = 5.2 (since it shifts from increase to decrease; or you could verify with second derivative). The actual ordered pair is (5.2, 526.0432)

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