# How do you find absolute extrema?

**Finding the Absolute Extrema**

- Find all critical numbers of f within the interval [a, b].
- Plug in each critical number from step 1 into the function f(x).
- Plug in the endpoints, a and b, into the function f(x).
- The largest value is the
**absolute**maximum, and the smallest value is the**absolute**minimum.

Besides, what is an absolute extrema?

**Absolute Extrema** If a function has an **absolute** maximum at x = b, then f (b) is the largest value that f can attain. A function f has an **absolute** minimum at x = b if f (b)≤f (x) for all x in the domain of f. Together, the **absolute** minimum and the **absolute** maximum are known as the **absolute extrema** of the function.

**relative extrema**will refer to the

**relative**minimums and maximums while

**absolute extrema**refer to the

**absolute**minimums and maximums. We will have an

**absolute**maximum (or minimum) at x=c provided f(c) is the largest (or smallest) value that the function will ever take on the domain that we are working on.

Also, can endpoints be absolute extrema?

**Absolute extrema** are the largest and smallest the function will ever be and these four points represent the only places in the interval where the **absolute extrema can** occur. In this example we saw that **absolute extrema can** and will occur at both **endpoints** and critical points.

1 Expert Answer Since f(x) is a polynomial function, the **number** of turning points (**relative extrema**) is, at most, one less than the degree of the polynomial. So, for this particular function, the **number of relative extrema** is 2 or less.