Question

for the polynomial function g , the rate of change of g is increasing for the x <2 and decreasing for x > 2. which of the following must be true?

Answer 1

Based on the information provided, if the rate of change of the polynomial function g is increasing for x < 2 and decreasing for x > 2, it implies that the function has a local minimum (or turning point) at x = 2.

The rate of change increasing to the left of x = 2 suggests that the function is rising, and the rate of change decreasing to the right of x = 2 suggests that the function is falling. Therefore, x = 2 is a point where the function transitions from increasing to decreasing, indicating a local minimum.

So, the statement "The function g has a local minimum at x = 2" must be true.