Problem 8

Given information

The given graph of the 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 and where   is undefined.
• 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 and where   is undefined is:

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