Answer to Question #256737 in Macroeconomics for natalie

Question

determine if the following functions is monotonic function 5x²+20x

and show the first derivative for its inverse

Answer 1

A monotonic function is one that is either entirely nonincreasing or entirely nondecreasing. A function is monotonic if the sign of its first derivative (which does not have to be continuous) does not change.

5x²+20x

Inverse = -5x² – 20x

Derivative = -10x – 20 = -x – 2

If F’(x) > 0 then f(x) is increasing

If F’(x) < 0 then f(x) is decreasing

Increasing (-2, ∞)

Decreasing (-∞, -2)

Decreasing: -∞ < x < -2, Increasing: -2 < x < ∞