Question

A(n) value of a polynomial is a value for which the polynomial is bigger

or smaller than any other nearby values.

Answer 1

A value of a polynomial where it is bigger or smaller than any other nearby values is called a critical point or an extremum.

Step-by-step explanation:

A value of a polynomial where it is bigger or smaller than any other nearby values is called a critical point or an extremum. This can be a maximum point (where the polynomial is bigger than neighboring values) or a minimum point (where the polynomial is smaller than neighboring values).

To find critical points, we can take the derivative of the polynomial and set it equal to zero. The values of x that satisfy this equation will give us the critical points.

For example, if we have the polynomial f(x) = x² - 4x + 3, we can find its critical points by taking the derivative f'(x) = 2x - 4 and setting it equal to zero: 2x - 4 = 0. Solving this equation, we find x = 2. Hence, the critical point of the polynomial is x = 2.

Answer 2

... local extreme ...

Step-by-step explanation:

A local extreme value of a polynomial is a value for which the polynomial is bigger or smaller than any other nearby values.

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If the extreme is larger than others nearby, it is a local maximum; if it is smaller than nearby values, it is a local minimum.