1. How do you know if the value found in a problem is a maximum value or a minimum value?
If the original function is a parabola examine the sign of x2. If it is negative, there will be a maximum involved.
Another way is to examine values either side of the stationary point.
A third way involves finding the second derivative. This helps determine the nature of the stationary values and points of inflection.
2. If the second derivative is positive, what does this mean?
If the second derivative is positive at the point where the first derivative is zero
this infers a MINIMUM point (concave up).If the second derivative is negative at the point where the first derivative is zero
this infers a MAXIMUM point (concave down).
