Calculus

A rectangle has width w inches and height h, where the width is twice the height. Both w and h are functions of time,t, measured in seconds. If A represents the area of the rectangle, what is the rate of change of A with respect to t at the instant where the width is 4 inches and the height is increasing at the rate of 2 inches per second?

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  1. width = twice height
    w = 2h or h = w/2

    area = wh = 2h^2
    A = 2h^2
    dA/dt = 4h dh/dt
    for the given data ... when w = 4, h = 2
    dA/dt = 4(2)(2) inches^2 /sec
    = 16 inches^2/sec

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    Reiny

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