How to Use the Function Max-Min Calculator
The Function Max-Min Calculator finds the maximum and minimum values of a quadratic function f(x)=ax²+bx+c over a closed interval [p, q]. On a closed interval, a quadratic's extreme values occur at the two endpoints, and at the vertex (x=-b/2a) when it falls inside the interval — so the tool compares the function's value at these points to find the answer. Entering 0 for coefficient a treats the function as linear and compares only the endpoints.
Enter coefficients a, b, and c along with the interval's start (p) and end (q), and the maximum and minimum values — along with the x-value where each occurs — appear instantly. If the start value is greater than or equal to the end value, the tool explains that the interval isn't valid. This is useful for checking max-min problems in math coursework or building intuition for optimization problems.
Frequently Asked Questions
On a closed interval, a quadratic function's max and min occur at the two endpoints, and at the vertex (x=-b/2a) if it falls inside the interval. The calculator compares the function values at these points to find the answer.
Yes, entering 0 for coefficient a treats the function as linear, comparing only the two endpoint values.
If the start value (p) is greater than or equal to the end value (q), the tool shows a message explaining that the interval isn't valid.