Thread: Need Help With a Tangent Line Problem

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

Originally Posted by erimat89

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

First find :

.

Thus, the slope of the line at is .

Thus, the tangent has the equation

Now find where it crosses the x axis:

.

It crosses the y axis when x=0.

So

Can you take it from here?

--Chris

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?

Originally Posted by erimat89

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

Originally Posted by erimat89

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

Makes alot of sense you clarified things for me. I've never been good with any sort of math problem that involves words for some reason I get thrown off.