find the equations of the two tangent lines of the graph of f that pass through the indicated points. f(x)=x^2 with points on it at (-1,-1),(3,) with an outside point at (1,-3)

Question

find the equations of the two tangent lines of the graph of f that pass through the indicated points. f(x)=x^2   with points on it at (-1,-1),(3,) with an outside point at (1,-3)

anonymous · Answer

(3,9) sorry left out the 9

anonymous · Answer

ok you want the line tangent to the graph of 
$$y=x^2$$ at the point 
$$(3,9)$$?  there is  only one, so not sure what that other condition is supposed to mean

anonymous · Answer

are you sure this is right?  (3,9) is on the graph because 
$$f(3)=3^2=9$$ so there is only one tangent line

anonymous · Answer

on the other hand 
$$(-1,-1)$$ is not on the graph, so you can find a line through (-1,-1) tangent to the graph.  that is a different problem all together

anonymous · Answer

i have this graphed out (x^2) and it has two points on it which are the ones i put above. with tangent lines going through them and they intersect at the (1,-3) point

anonymous · Answer

oh and i meant (-1, 1)

anonymous · Answer

ok 
$$f(-1)=1$$ so that point is on the graph of 
$$y=x^2$$ the tangent line at that point has slope -2, since the derivative of x^2 is 2x
the line will therefore have the equation 
$$y-1=-2(x+1)$$ or 
$$y=-2x-1$$ but there is only one line tangent to the curve there.

anonymous · Answer

likewise at (3,9) the slope will be 6, and so the line will be 
$$y-9=6(x-3)$$

anonymous · Answer

how do you know the slope is 6?