Question

I need to give an equation for an absolute value function that has a minimum. How do I determine that it has a minimum?.

Answer 1

To determine the minimum of an equation, we derive the equation using differential calculus twice (or simply take the second derivative of the function). If the second derivative is greater than 0, then it is minimum; else, if it is less than 1, the function contains the maximum. If the second derivative is zero, then the inflection point is identified.