Precalculus

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a farmer has available 1032 feet of fencing and wishes to enclose a rectangular area. If x represents the width of the rectangle for what value of x is the area the largest
A) 256.5 feet b) 258 feet
c) 256 feet d) 257 feet
please show work!
i need help fast

  • Precalculus -

    Let L=total length of fencing.
    x=width
    (L/2-x)=length
    A(x)=Area=x(L/2-x)
    Differentiate A with respect to x, and equate A'(x) to zero and solve for x=x0 which gives the maximum or minimum area.
    Differentiate A'(x) again to get A"(x).
    Confirm that A"(x0) is negative for a maximum (and positive for a minimum).

    You should find that x0=width=length.

    Post your answer for a check if you wish.

  • Precalculus -

    is it 258

  • Precalculus -

    Yes, that's correct.

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