Question

f(x) is a polynomial function that is increasing when x³, decreasing when -1 & lt; x & lt; 3. What would be the function from these characteristics? What would graph look like?

Answer 1

A possible equation of the polynomial is f(x) = a (x - p) (x - q) (x - r)

The graph of this polynomial would show increasing behavior as x becomes larger, and it would have local minima between -1 and -3 where it decreases.

How to find the equation

Increasing when x³

This means that the function is increasing as x takes on larger positive values. The degree of the polynomial must be at least 3, and the leading coefficient is positive.

Decreasing when -1 < x < 3

In the given interval, the function is decreasing. This implies that there is a root (zero) of the function between -1 and 3.

Combining these characteristics we have

f(x) = a (x - p) (x - q) (x - r)