Final answer:
The slope of the tangent line to the parabola y=3x-x^2 at the point (3,0) is -3.
Step-by-step explanation:
To find the slope of the tangent line to the parabola y=3x - x^2 at the point (3,0), we need to calculate the derivative of the function, which gives us the slope of the tangent line at any point on the curve.
The derivative of y with respect to x is found by using the power rule:
y' = d/dx(3x - x^2) = 3 - 2x
Now, we substitute x = 3 into the derivative to find the slope at the given point:
y'(3) = 3 - 2(3) = -3
The slope of the tangent line to the parabola at the point (3,0) is therefore -3.