Connected Rates of Changes?

A point is moving along the curve. At the point P the y-coordinate is increasing at half the rate

at which the x-coordinate is increasing. Find the x-coordinate of P.

Eqn of curve is : y = (3x + 4)^1/2

2 Answers

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  • 4 weeks ago
    Favorite Answer

    dy/dt = (3/2)(dx/dt)(3x + 4)^(-1/2), by the use of the power and chain rules.

    (dy/dt) / (dx/dt) = (3/2)(3x + 4)^(-1/2)

    1/2 = (3/2)(3x + 4)^(-1/2)

    1 = (3)(3x + 4)^(-1/2)

    1/3 = (3x + 4)^(-1/2)

    1/3 = 1 / (3x + 4)^(1/2)

    (3x + 4)^(1/2) = 3

    (3x + 4) = 9

    3x = 5

    x = 5/3

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  • Ian H
    Lv 7
    4 weeks ago

    dy/dx = (1/2)*3/√(3x + 4) = 1/2 

    9 = 3x + 4, so, x = 5/3 

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