Question

Consider the curve y = x − x^3, find the slope of the tangent line to the curve at the point (1, 0).

Answer 1

The derivative of a function, such as the one given above, represents the slope of the tangent line to the curve at the given point.

In this case, y = x − x^3, and dy/dx = 1 - 3x^2.  Letting x = 1, we get the slope of the tangent line at the point (1,0):  1 - 3(1^2) = -2 (answer)