jess asked in Science & MathematicsMathematics Β· 1 month ago

The function 𝑓(π‘₯)=2π‘₯^3βˆ’27π‘₯^2+108π‘₯βˆ’11 has two critical numbers.?

The smaller one equals(blank) and the larger one equals(blank)Β 

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  • 1 month ago
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    critical values occur when the derivative of the function equals 0

    so f'(x) = 6x^2 - 54x + 108 = 0

    ==>x^2 - 9x + 18 = 0

    ==> (x-3)(x-6) = 0

    ==> x = 3 or x = 6

    in addition:

    f"(x) = 12x - 54

    f"(3) = 36 - 54 = - 18 ==> a maximum

    f"(6) = 72 - 54 = 18 ==> a minimum

    will leave it to you to find f(3) and f(6)

    and work out the rest of the answer.

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