High School Math : Identifying Slope at a Point

Example Questions

Example Question #1 : Calculus I — Derivatives

Find the slope of the line tangent to the -intercept of the parabola:

Explanation:

To find the slope of a line tangent to a parabola at a specific point, find the derivative of the parabola's equation, then substitute the -coordinate of the specific point in the new equation.

In this case, it helps to expand the equation before taking the derivative:

Now take the derivative of the expanded equation:

Since the -intercept is the point where the -coordinate is , substitute  into the equation for .