Question

Slope of Curve y = 1/x, P(-2, -1/2)

A) Use numerical methods for integration.
B) Apply the midpoint formula.
C) Compute the derivative at the given point.
D) Solve a system of linear equations.

Answer 1

The slope of the curve y = 1/x at the point P(-2, -1/2) is -1/4.

Step-by-step explanation:

To find the slope of the curve y = 1/x at the point P(-2, -1/2), we can use the derivative of the function. The derivative of y with respect to x is given by dy/dx = -1/x^2. To find the slope at P(-2, -1/2), we substitute x = -2 into the derivative: dy/dx = -1/(-2)^2 = -1/4. Therefore, the slope of the curve at P(-2, -1/2) is -1/4.