Problem 4c

Given information

The given graph of the derivative  of a function  is:

The given condition is that .

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  by mentioning the intervals where the function is increasing and decreasing by using the fact that in increasing where and decreasing where .