Final answer:
The slope of a curve at point P on the function y = x² is found by taking the derivative of the function, which gives 2x. At point P, the slope of the tangent is 2 times the x-coordinate of point P.
Step-by-step explanation:
The slope of a curve at a specific point is the same as the slope of the tangent line to the curve at that point. To find the slope at point P on the curve y = x², we need to use calculus, specifically the concept of a derivative. The derivative of a function gives us the slope of the tangent line at any given point.
For the function y = x², the derivative y' = 2x. To find the slope at a specific point P with an x-coordinate (let's call it a), we simply plug a into the derivative. Therefore, the slope at point P is 2a.
To illustrate this with an example, if point P has the coordinates (3, 9), the slope of the tangent line at P would be y' = 2 * 3 = 6.