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i have confused in one topic and please help me,suppose that we have following function $f(x)=x^3+x^2-2*x-3)$ we know that there is a tangent of this function which goes through point $(1,-3)$,we are required to find abscissa,where this tangent intersect ox axis. what i have tried first it to find derivative,so we have ($f(x)'=3*x^2+2*x-2)$,now what does mean abscissa of intersection of tangent line with ox axis?if it means that,it includes every point where y=0,then answer is this

http://www.wolframalpha.com/input/?i=3*x%5E2%2B2*x-2%3D0

but if it is y value at $x=0$,then answer is $-2$,so i am confused about this and please help me,also what i should do if instead of ox axis,,we are required to find ordinate of intersection of tangent line with oy axis?

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up vote 1 down vote accepted

The derivative gives the slope of the tangent line at that point. In your case, if you evaluate $f'(1)$ you get $3$. The tangent line is then the line through $(1,-3)$ with slope $3$. The point-slope form of the line is then $y-(-3)=3(x-1)$. On the $x$ axis, $y=0$, so you substitute that in to find $x$.

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so it means that,ordinate of oy axis intersection would be at x=0? –  dato datuashvili Jun 3 '12 at 20:23
    
@dato: Correct. –  Ross Millikan Jun 3 '12 at 20:33
    
thanks @ Ross Millikan ,good night –  dato datuashvili Jun 3 '12 at 20:46
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