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CALCULUS

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Find and Classify, the absolut extreme values of each function on the given interval.(do not give decimal)

(a) g(x)= 2sinx + 2cos^(2)x; [0,2pie]
(b) f(x)=x^(4)-2x^(3)+3; [-1,2]

  • CALCULUS - ,

    Set the derivatives equal to zero to determine the location of the extreme values.

    Determine what the second derivative is at those points to tell maxima from minima. (Positive second derivative means a minimum). If the second derivative is zero, the situation is more complex. You might try plotting it out.

    For example, in (b),
    f'(x) = 4x^3 -6x^2 = 0
    x^2(4x - 6) = 0
    x = 0 or 3/2
    f"(x) = 12x^2 -12x
    When x = 3/2, f"(x) = 9
    So x = 1.5 is a minimum location

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