aimforthehead Posted November 21, 2012 Share Posted November 21, 2012 I'm reviewing a calculus test I took and ran into this problem, which I got right but don't remember how... Find the equation of the tangent line to the curve y = f(x) which is parallel to the line 3x - 4y = 1 y = 3/4x - 1/4 So my answer was y = 3/4x + 5/4, where did the 5/4 come from? Without points how can we find what b is? Or am I missing information from the problem you think? Thanks. Link to comment Share on other sites More sharing options...

mathematic Posted November 21, 2012 Share Posted November 21, 2012 You need to specify f(x). For what x is f'(x) = 3/4? Next find the tangent line at that point on f(x). Link to comment Share on other sites More sharing options...

aimforthehead Posted November 22, 2012 Author Share Posted November 22, 2012 I'm afraid I still don't understand...I just got into anti-derivatives so my first guess is f(x) = 3/4x...but that isn't a curve, so I don't know. Link to comment Share on other sites More sharing options...

mathematic Posted November 22, 2012 Share Posted November 22, 2012 I'm afraid I still don't understand...I just got into anti-derivatives so my first guess is f(x) = 3/4x...but that isn't a curve, so I don't know. The problem statement is incomplete. You need a specific f(x)! Link to comment Share on other sites More sharing options...

imatfaal Posted November 23, 2012 Share Posted November 23, 2012 aimforthehead - these sorts of situations it is very useful to draw a quick sketch. It might show you two things that as mathematic keeps telling you - the question is incomplete (you need at least one point on the line y=f(x). There are an infinite number of curves that are tangent to a line parallel to your function. Talking about tangents to straight lines is also a little weird as well - the tangent to a straight line is the line itself; we normally refer to tangents when talking about actual curves, the tangent is the line that touches the curve and thus has the same instantaneous slope as the curve at that point. Link to comment Share on other sites More sharing options...

SamBridge Posted January 12, 2013 Share Posted January 12, 2013 (edited) I'm reviewing a calculus test I took and ran into this problem, which I got right but don't remember how... Find the equation of the tangent line to the curve y = f(x) which is parallel to the line 3x - 4y = 1 y = 3/4x - 1/4 So my answer was y = 3/4x + 5/4, where did the 5/4 come from? Without points how can we find what b is? Or am I missing information from the problem you think? Thanks. Wait, f(x)=y? That would mean the derivative is always 3/4. Unless you mean f'(x) or f''(x) is 3/4x-1/4, there shouldnt be a curve. Edited January 12, 2013 by SamBridge Link to comment Share on other sites More sharing options...

John Posted January 24, 2013 Share Posted January 24, 2013 (edited) The idea is that f(x) is some curve such that at some point on the curve, the tangent is parallel to the (otherwise unrelated) line 3x - 4y = 1 => y = (3/4)x - 1/4. As imatfaal has directly and mathematic has indirectly pointed out, there are infinitely many curves that have this property. Therefore, the answer to the OP's question depends on what, exactly, f(x) is. Edited January 24, 2013 by John Link to comment Share on other sites More sharing options...

JMessenger Posted January 31, 2013 Share Posted January 31, 2013 I'm reviewing a calculus test I took and ran into this problem, which I got right but don't remember how... Find the equation of the tangent line to the curve y = f(x) which is parallel to the line 3x - 4y = 1 y = 3/4x - 1/4 So my answer was y = 3/4x + 5/4, where did the 5/4 come from? Without points how can we find what b is? Or am I missing information from the problem you think? Thanks. From the looks of it, anything about f(x) or tangents is extraneous. You were actually only asked to find an equation of a line that is parallel to another line. By changing nothing more than the y intercept on the given line equation, you found "the equation of the...line..parallel to the line...". It sounds like a trick question designed to test your reading comprehension, which you got correct. You could have substituted any number in place of 1/4. Link to comment Share on other sites More sharing options...

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