Calculus Homework Help

Question

what is the instantaneous slope of y = 6/x at x = -2?

Answer 1

First you need to find the slope. It is found from the derivative of y wrt to x as y can be written as y = 6.x^-1

slope = dy/dx = y' = (-1)(6)x^-1-1(1) = -6.x^-2 = -6/x² , substituting x = -2, y' = -6/(-2)² = -6/4 = -3/2 is the instantaneous slope of the line at the point x = -2

Answer 2

y = 6/x at x=-2

y' = slope = derivative of 6/x = the derivative of 6x^-1 = -6x^-2 = -6/x^2

at x=-2

y'(-2) = -6/(-2)^2 = -6/4 = -3/2 = -1.5