Use the method of example 3 to find a general expression

Question

Use the method of Example 3 to find a general expression for the slope of a tangent line to each of the indicated curves. Then find the slopes for the given values of x. Sketch the curves and tangent lines.

EXAMPLE 3 Slope of tangent line at general point

Find the slope of a line tangent to the curve of y = 4x - x² at the point (x₁, y₁) The points P and Q are

 therefore

Here, we see that  therefore.