Minimum and Maximum of Quadratic on an Interval

Minimum and Maximum of Quadratic on an Interval

## Definition / Concept

For a quadratic restricted to an interval, the extremum depends on whether the vertex lies inside the interval.

## Formula

For:

$$f(x)=ax^2+bx+c$$

the critical point is:

$$x=-\frac{b}{2a}$$

If the critical point lies inside the interval, evaluate the quadratic there and at the endpoints.

If the critical point lies outside the interval, the extrema occur at the endpoints.

## Usage

- Used in JEE Main problems involving maximum or minimum values over a restricted domain.