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Optimization

AP Calculus AB· difficulty 3/5

x A 2x

A rectangle is inscribed under the parabola y=9−x2y = 9 - x^2 with width 2x2x. What is the area A(x)A(x)?

  • A

    2x(9−x2)2x(9-x^2)

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  • B

    9−x39-x^3

  • C

    x(9−x2)x(9-x^2)

  • D

    (9−x2)2(9-x^2)^2

Explanation

Width =2x= 2x and height =9−x2= 9-x^2, so A=2x(9−x2)A = 2x(9-x^2).

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