Consider the parabola y = 8x – x². Find the slope of the tangent line to the parabola at the point (1, 7).

To find the slope of the tangent line to the parabola at the given point (1, 7), we first need to determine the derivative of the function. The equation of the parabola is given as y = 8x – x².

We differentiate this equation with respect to x to find the slope:

dy/dx = d/dx (8x - x²) = 8 - 2x

Now, we will evaluate the derivative at the given x-coordinate, which is 1:

dy/dx at x = 1 = 8 - 2(1) = 8 - 2 = 6

Therefore, the slope of the tangent line to the parabola at the point (1, 7) is 6.