Could someone please help me with the following problem I'm having difficulties with.
1) Show that the tangent line to the parabola y=Ax^2, A not equal to 0, at the point x=c will intersect the x-axis at the point (c/2, 0)
2) Determine where this line intersects the y-axis
Maybe I'm just confused but the question wasn't asking where it intersected the x-axis the x-axis intersection is given at the point (c/2, 0) it was only asking to determine where it crossed the y-axis in part 2 of the question. Why is this point (c/2, 0) given?
It asks you to show that the line intersects the x-axis at the point (c/2,0).
Since I got the equation of the line to be , at y=0, the line crosses the x-axis.
Thus . So we see that it crosses the x-axis at
Now, it intersects the y axis when x=0. Thus, we see that .
Thus, the y intercept is .
Does this make sense?
--Chris