Question

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

Answer 1

1. Final answer:
2. The slope of the tangent line to the parabola at the point (1, 3) is 2, which is found by differentiating the function and evaluating it at x = 1.
4. Step-by-step explanation:
5. To find the slope of the tangent line to the parabola y = 4x - x² at the point (1, 3), we need to calculate the derivative of the function, which will give us the slope of the tangent line at any point x. The derivative of y = 4x - x² with respect to x is dy/dx = 4 - 2x. Plugging in the x-coordinate of the given point, we get dy/dx at x = 1 is 4 - 2(1) = 2. Therefore, the slope of the tangent line at the point (1, 3) is 2.