Question

How to find slope of parabola at a point?

Answer 1

To find the slope of a parabola at a specific point, you need to find the tangent line to the parabola at that point and calculate the slope between two points on the tangent line.

Step-by-step explanation:

The slope of a parabola at a specific point can be found by finding the slope of a straight line tangent to the parabola at that point. To do this, you need to follow these steps:

1. Find the tangent line to the parabola at the given point.
2. Determine the endpoints of the tangent line, which correspond to two points on the parabola.
3. Use the formula for slope (change in y divided by change in x) to calculate the slope between these two points.

Answer 2

To find the slope of a parabola at a point you have to find is the first derivative of the function. This first derivative is the slope of the tangent of the parabola at the given point and it is the same slope of the parabola.

If you have the parabola with the general form y = Ax^2 + Bx + C

The slope at point (m,n) is:

y' = 2Ax + B

x = n

=> y ' = 2A(n) + B.

For example, find the slope of the parabole y = 3x^2 + 2x + 1, at x = 1


y' = 6x + 2

x = 1 => y' = 6(1) + 2 = 8.

So the slope at x = 1 is 8.