August 27th, 2009, 04:09 PM  #1 
Senior Member Joined: Apr 2009 Posts: 201 Thanks: 0  clarification help...
Hey, there's something I'm confused about from my textbook, I was hoping that you guys could help me: It's about finding the union points between a tangent line and some function.. If the function is x^2, dy/dx f(a) = 2a. g(x) = 2a(xa)+a^2 = 2axa^2 x^2 = 2ax  a^2 (x^2  2ax + a^2 ) = 0 (x  a ) ^2 = 0 , x = a I don't understand the 2a(xa)+a^2 part.. if you wanted to have the equation of the tangent line, wouldn't y= a^2 when x = a? but here, the equation has a^2 as it's "b" in mx+b and "x" is substituted with (xa).. I'm confused.. The equation should look like like 2a(x)  a^2 from the beginning, if x=a, y=a^2 thanks :S 
August 27th, 2009, 04:56 PM  #2 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: clarification help...
Hint: What does the distributive axiom say about the expression 
August 27th, 2009, 05:04 PM  #3  
Senior Member Joined: Apr 2009 Posts: 201 Thanks: 0  Re: clarification help... Quote:
Sorry, I can be slow sometimes but thanks for replying  
August 28th, 2009, 01:56 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,104 Thanks: 1907 
The author probably had in mind the point–slope form of the equation of a line rather than the slopeintercept form.

August 28th, 2009, 05:46 AM  #5 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: clarification help...
The author might have wanted readers to practice using the distributive axiom in finding the solution. Here's another hint. The distributive axiom states that for any , . For example, to get of we can just get of and of . Applying the distributive axiom to , we obtain 
August 29th, 2009, 11:40 AM  #6 
Senior Member Joined: Apr 2009 Posts: 201 Thanks: 0  Re: clarification help...
Ah, I've got the idea. Thanks guys. I just never seen the slope point form before, but it makes sense: the change in y is the change in x times the slope


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