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  1. #1
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    Exclamation minimum values

    This is a practice exam problem am stuck on


    Find the max and min values of the fuction f(x)=x^3-9x^2+15x+3 on intervals [0,2]
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  2. #2
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    Quote Originally Posted by Math Phobe View Post
    This is a practice exam problem am stuck on


    Find the max and min values of the fuction f(x)=x^3-9x^2+15x+3 on intervals [0,2]

    The global extrema of a function on a closed interval are either calculus type local extrema in the interior of the interval or occur at the end points of the interval.

    So first look at the solutions of:

    f'(x)=3x^2-18x+15=0

    these are the roots of x^2-6x+5=0, which are x=5 and x=1, x=5 is not in the interval so we can ignore it, so now we need only consider

    f(0),\ f(1) and f(2),

    f(0)=3,
    f(1)=1-9+15+3=10
    f(2)=8-36+30+3=5

    so the global minimum on [0,2] is 3 and the global maximum is 10 and these occur when x=0 and x=1 respectivly.

    RonL
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