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Calculus

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The edge of a cube is increasing at a rate of 2 inches per minute. At the instant when the volume is 27 cubic inches, how fast is the volume changing? indicate the units of measure. V=x^3

  • Calculus - ,

    dx/dt = 2 inches/min
    V = x^3
    so,
    dV/dt = 2^3 = 8 cubic inches/min

  • Calculus - ,

    V = x^3
    dV/dt = 3x^2 dx/dt

    when V= 27, x = 3, dx/dt = 2

    dV/dt = 3(3^2)(2) cubic inches/min
    = 54 cubic inches/min

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