Find the slope of the tangent line to the parabola y = 4x – x² at the point (1, 3)

To find the slope of the tangent line to the given parabola at the specified point, we need to follow these steps:

1. Start with the equation of the parabola: y = 4x – x².
2. Differentiate the equation with respect to x to find the derivative (dy/dx). This derivative represents the slope of the tangent line at any point on the parabola.

The differentiation process gives us:

 dy/dx = d(4x)/dx - d(x²)/dx = 4 - 2x.

This means that the slope of the tangent line at any point (x, y) on the parabola can be found by substituting the x value of that point into the derivative.

Next, we substitute x = 1 into the derivative:

 dy/dx = 4 - 2(1) = 4 - 2 = 2.

This gives us the slope of the tangent line at the point (1, 3): 2.

So, the slope of the tangent line to the parabola at the point (1, 3) is 2.