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How to show non-negative tangents ?

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data
    1. Show that there are no tangents to the graph of [tex]f(x) = \frac{5x+2}{x+2}[/tex] that have a negative slope.

    2. Determine the equation of the tangent to the curve [tex]y = \frac{x^{2}-1}{3x}[/tex] at x = 2

    2. Relevant equations
    1. Our teacher told us not to use the quotient rule because it is not in our curriculum so please do not give me a solution using the quotient rule. Thanks.
  2. jcsd
  3. Sep 28, 2008 #2


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    Gold Member

    What about using the product rule with the chain rule then? Use the fact that A/B=AB-1.
  4. Sep 29, 2008 #3

    Gib Z

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    Homework Helper

    1. Or Perform Polynomial division on f(x), then its quite simple.

    2. You need 3 pieces of information for a tangent - what are they?
  5. Sep 29, 2008 #4
    for 1. dont i use inequality ? set the equation f(x) < 0 and solve for x if it cant be solved then u can conclude there are no points that can give me a negative tangent
  6. Sep 29, 2008 #5


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    If you solve f(x)<0, you will be finding all x for which the function itself is negative i.e. below the x axis. But thats not what you want to find, you need to show that the DERIVATIVE is never negative.
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