Question

I beg for someone. I need a maximum, minimum, domain, and range of polynomial:

B(x) = (x-5)^2 (x+2)^2 (x)^2 (x-3) ?

Answer 1

• domain: all real numbers, (-∞, ∞)
• range: all real numbers, (-∞, ∞)
• maximum: +∞
• minimum: -∞

Explanation:

The function is an odd-degree polynomial. The domain and range of any odd-degree polynomial is (-∞, +∞). It has no finite maximum or minimum.

There are 3 local maxima, and 3 local minima. The ones that are non-zero are irrational. Those are about -150.018, -580.455, and 578.545. If you're seriously expected to solve for these values, no doubt you have been given a method for doing so. Use that method.

These local extreme values are reported by the Desmos on-line graphing calculator.