Problem 12

Given information

The given graph of the population function is:

Step-by-step explanation

• The function   is said to be increasing function in an interval if   for that interval and the function   is said to be decreasing function in an interval if    for that interval.
• The function   has inflection point where   that is the function   has inflection point where the slope of the tangent to the curve is 0
• The function   is said to be concave upwards in an interval if   for that interval and the function   is said to be concave downwards in an interval if   for that interval. In other words, the function   is said to be concave upwards in an interval if   is increasing in that interval and the function   is said to be concave downwards in an interval if   is decreasing in that interval.
• Draw the graph of the function  by mentioning the intervals where the function is increasing and decreasing.
• Draw the graph of the function   by mentioning the intervals where the function is concave upwards and concave downwards.

The graph of the function  mentioning the intervals where function is increasing and decreasing is:

The graph of the function   mentioning the intervals where function is concave upwards and concave downwards is: