194k views
5 votes
Find the slope of the tangent line to the parabola y=3x-x^(2) at the point (3,0)

User Amrx
by
8.2k points

1 Answer

4 votes

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.

User Frenchcooc
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories