Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 weeks ago

 Find the absolute maximum and absolute minimum values of the function 𝑓(𝑥)=𝑥^3+6𝑥^2−63𝑥+11 over each of the indicated intervals.?

Some one please help. I only got two right. 

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3 Answers

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  • 3 weeks ago
    Best Answer

    f(x) = x³ + 6x² - 63x + 11

    absolute minimum or maximum can occur at stationary points or at endpoints

    f(x) = x³ + 6x² - 63x + 11

    f'(x) = 3x² + 12x - 63

    3x² + 12x - 63 = 0

    x² + 4x - 21 = 0

    x = -7, x = 3

    ( a )

    endpoints: x = -8 and x = 0

    but 3 is outside the interval

    f(-8) = 387

    f(-7) = 403

    f(0) = 11

    ∴ 

    ( 1 ) absolute maximum = 403 

    ( 2 ) absolute minimum = 11

    ( b )

    endpoints: x = -5 and x = 4

    but -7 is outside the interval

    f(-5) = 351

    f(3) = -97

    f(4) = -81

    ∴ 

    ( 1 ) absolute maximum = 351

    ( 2 ) absolute minimum = -97 

    ( c )

    endpoints: x = -8 and x = 4

    but -7 is outside the interval

    f(-8) = 387

    f(-7) = 403

    f(3) = -97

    f(4) = -81

    ∴ 

    ( 1 ) absolute maximum = 403

    ( 2 ) absolute minimum = -97

  • rotchm
    Lv 7
    3 weeks ago

    Apply the exact same procedure already given to you in:

    https://ca.answers.yahoo.com/question/index?qid=20...

  • ted s
    Lv 7
    3 weeks ago

    So YOU looked at f ' to see where it was equal to 0....the smallest would yield a local max and the larger a local min....if on a closed interval then you checked the function values at the endpoints...CORRECT ??....if not then DO it now.

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