Consider the following function:

f(x)=abxcf(x)=abxc

where a, b, c are non-negative integers and -1 < x < 1

Statement I:Regardless of the values of a, b, and c, this function has no local maxima.

Statement II:If c = 3 and b 00, then there is an inflection point at x = 0, regardless of the value of a

Statement III:if c = 4 and b = 1, then there is an inflection point at x = 0, regardless of the value of a

State whether each statement is true or false. Explain your answer. If the statement is false, you may either explain why it is false, or provide a counter example to the statement.[Max 50 words per statement]