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Equation of a curve passing through (1,2)

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    A curve has slope 2x + 3 at each point (x, y) on the curve. Which of the following is an equation for this curve if it pases through the point (1,2)?

    Answer: y= x2 + 3x - 2

    2. Relevant equations

    y= mx + b

    3. The attempt at a solution

    If the slope is 2x + 3, then that means it is the derivative. Since I a point (1,2), I can find m and b.

    m = 2(1) + 3 = 5​

    Thus,

    2 = 5(1) + b
    b = -3​

    Therefore, my equation is

    y= 5x - 3​

    But this isn't correct. What am I doing wrong?
     
  2. jcsd
  3. May 2, 2010 #2

    vela

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    You found the equation of the tangent to the curve at (1,2), not the equation of the curve.
     
  4. May 2, 2010 #3
    i agree.
    To find the equation of the curve you will be doing some integration.
     
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