Science:Math Exam Resources/Courses/MATH100/December 2013/Question 08 (d)/Solution 1

From UBC Wiki

From parts (a), (b), and (c) we know the following about :

  • The critical numbers of (where is zero or does not exist) are
  • is increasing on and decreasing on
  • has a local minimum at and a local maximum at (note the change in the increase/decrease of )
  • is concave up on and concave down on
  • has an inflection point (changes concavity) at


  • and thus has x-intercepts at


  • and , thus the graph of is very steep near


Plotting the points of interest gives the following:

Math 100 December 2013 Question 8(d) Step 1.png


Accounting for increase and decrease gives the following rough sketch:

Math 100 December 2013 Question 8(d) Step 2.png


Finally, incorporating concavity leads us to the final graph: