Line Tangent ro a Parabola

  1. 1. The problem statement, all variables and given/known data
    Find the point on the parabola y= 4x^2 + 2x - 5 where the tangent line is perpendicular to the line 3x + 2y = 7.


    2. Relevant equations



    3. The attempt at a solution
    I don't know what to do since I was away the last 3 classes since I was away. Help me please.
     
  2. jcsd
  3. You want to find the slope of the line you're given and use the definition of a derivative as well as perpendicularity to solve for the x value you want.
     
  4. Two perpendicular lines have slopes that are negative reciprocals of each other, eg: a line with a slope 2 is perpendicular to a line with a slope -1/2.

    Find the slope of the line, find the negative reciprocal of that slope. The derivative of a function is the slope of that graph at any point on the graph, so find the derivative of the parabola and see at what value of x it will equal the negative reciprocal of the slope you found earlier.
     
  5. So I take the slope of this? 3x + 2y = 7

    so.....

    2y = -3x + 7
    y= -3/2x + 7/2

    slope = -3/2 so if it is perpendicular the slope is 2/3 is that my right slope?

    I now I have to do more but it that right so far?
     
  6. Yes.
     
  7. Correct.

    dy/dx = 8x+2
    You want the value of x when dy/dx is (2/3), as you said from above.
    Solving for x gets (-1/6).
    Plug this value into your original equation y=4x^2 etc.
     
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