# Calculus slope intersection

• Sep 1st 2009, 03:48 PM
pantera
Calculus slope intersection
Can someone show me how to find the points that intersect with the graph of the function f(x) = 1-x^2 and the tangent line that goes through the point (2,0).
• Sep 1st 2009, 04:01 PM
luobo
Quote:

Originally Posted by pantera
Can someone show me how to find the points that intersect with the graph of the function f(x) = 1-x^2 and the tangent line that goes through the point (2,0).

The point is on the curve $f(x)=1-x^2$. Say the point is $(a,1-a^2)$. The slope of the tangent line is $k=f'(a)=-2a$. So the tangent line is
$f(x)=-2a(x-a)+1-a^2=-2ax+1+a^2$
The line passes through the point $(2,0)$, then $0=-4a+1+a^2$
Therefore, $a= 2\pm\sqrt{3}$
• Sep 1st 2009, 04:13 PM
pantera
Thank you so much!