Problem 9

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.
• If the function is linear, then the value of is constant.

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