Final answer:
The slope of the tangent to the curve y - 1 = x² at the point where x = a is found by differentiating the equation to get dy/dx = 2x and then substituting x with a, yielding a slope of 2a.
Step-by-step explanation:
To find the slope of the tangent to the curve y - 1 = x² at the point where x = a, we would differentiate the equation with respect to x to find the derivative. The derivative of a function at a point gives us the slope of the tangent line at that point. Differentiating y - 1 = x², we get:
dy/dx = 2x
Then, substituting x = a into the derivative gives us the slope of the tangent:
slope at x = a = 2a
This derivative represents the rate of change of y with respect to x at any point x on the curve. Specifically, for x = a, the slope of the tangent line to the curve would be 2a.