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Homework Help: Two calc problems

  1. Feb 26, 2006 #1
    PV = C (Boyle's Law)

    At a certain instant, the volume is 480 cm^3, the pressure is 160 kPa, and the pressure is increasing at a rate of 15 kPa/min. At what rate is the volume decreasing at this instant?


    Find the equations of both lines that pass through the point (2, 3) and are tangent to the parabola y = x^2 + x.

    I don't really know where to start with these...
  2. jcsd
  3. Feb 26, 2006 #2


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    [tex]PV=C\Rightarrow\frac{d}{dt}(PV)=\frac{d}{dt}C\Rightarrow \frac{dP}{dt}V+P\frac{dV}{dt}=0[/tex]

    then plug-in the known values of P,V, and dP/dt to solve for dV/dt.
  4. Feb 27, 2006 #3


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    Any line through (2, 3) can be written as y= m(x- 2)+ 3 for some m.

    If (x,y) is a point where that line intersects the parabola y= x2+ x, then we must have m(x-2)+ 3= x2+ x. If, in addition, the line is tangent to the parabola there, we must have
    m= 2x+ 1. Solve those two equations for x and m.

    I've edited this: before I had m= 2x- 1. Obviously, the derivative of x2+ x is 2x+ 1, not 2x- 1.
    Last edited by a moderator: Feb 28, 2006
  5. Feb 27, 2006 #4
    Thank you.
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