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Tangent line

  1. Mar 13, 2010 #1
    For what value of b is the line y = 10x tangent to the curve y = e[tex]^{bx}[/tex] at some point in the xy-plane?

    y' = b*e[tex]^{bx}[/tex] = 10x

    How can I solve for b here?
     
  2. jcsd
  3. Mar 13, 2010 #2

    jbunniii

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    Your equation isn't right.

    What condition(s) must be satisfied if [itex]y = 10x[/itex] is tangent to [itex]y = e^{bx}[/itex] at some point?
     
  4. Mar 13, 2010 #3
    It has to be the derivative.
     
  5. Mar 13, 2010 #4

    jbunniii

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    What has to be what derivative? Try to be precise when you are expressing ideas in mathematics.

    Say I have two differentiable functions, [itex]f(x)[/itex] and [itex]g(x)[/itex]. What must be true if [itex]g[/itex] is tangent to [itex]f[/itex] at some point [itex]x_0[/itex]?
     
  6. Mar 13, 2010 #5
    I already solved for the derivative in my 1st post and set it equal to the tangent equation since the derivative needs to equal that to satisfy the problem. The problem was that I have b times e to the b where I need to solve for b.
     
  7. Mar 13, 2010 #6

    jbunniii

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    As I already said, your equation is wrong, so there is no point trying to solve it for b.

    Can you explain why you set the derivative of the exponential equal to 10x?
     
  8. Mar 13, 2010 #7
    That is what I need the derivative to be equal.
     
  9. Mar 13, 2010 #8

    jbunniii

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    No it's not.

    What properties of a curve and a line must be equal if the line is to be tangent to the curve at a point?
     
  10. Mar 13, 2010 #9
    We can keep going around and circles all day but it isn't going to get anywhere.
     
  11. Mar 13, 2010 #10

    jbunniii

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    OK, good luck.
     
  12. Mar 14, 2010 #11
    "We" ? You are the one thinking in circles, jbunniii is actually trying to point you the way out of your circles, but it seems you just don't want to listen...
     
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