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Math Help - (c,f(c)) doesn't need to be given when finding eqn's of tangent lines, just c right?

  1. #1
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    (c,f(c)) doesn't need to be given when finding eqn's of tangent lines, just c right?

    When asked to find the equation of a tangent line for a function at a particular (c, f(c)) then f(c) doesn't need to be given because it's really just coming from plugging c into f(x) right?
    Even though, I'm nearly sure I'm right about this I ask just because it seems strange that this question isn't being asked by only giving you the particular x coordinate.

    For example I was asked to find the equation of the tangent line for f(x) = x^2 at the point (2,4). But the question could have just asked find the equation of the tangent line for f(x) = x^2 when x is 2?
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  2. #2
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    Since you need both coordinates of the point to write an equation of the tangent line, someone is going to have to supply the y-value. That they do it for you is just a plus!
    (But you're right - you could have found that on your own, and m = dy/dx doesn't depend on y)
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    You're correct; there's sometimes redundancy in the wording of these types of questions. A situation where you might need to specify the y coordinate is when the function is defined implicitly. Then there may be several solutions for a given value of x.
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    Quote Originally Posted by ojones View Post
    You're correct; there's sometimes redundancy in the wording of these types of questions. A situation where you might need to specify the y coordinate is when the function is defined implicitly. Then there may be several solutions for a given value of x.
    which would mean the equation is just a relation and not a function, right?
    so for example, if we were given the relation x^2 + y^2 = 25 and if we were only interested in the principal square root when solved for y: y= sqrt(25-x^2) . I see what you mean if they just gave you the relation then they would have to give a point such as (3,4) as opposed to just an x-coordinate of 3.
    Last edited by lamp23; April 7th 2011 at 09:08 PM.
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  5. #5
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    Correct. A common question in the topic of implicit differentiation is to ask for the equation of a tangent line at some point (x,y). Specifying x alone wouldn't be enough.
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