Curve sketching
0/10
Examples
Lessons
- Use the guidelines to sketch the graph of:
f(x)=x3+8x3−8 - Use the guidelines to sketch the graph of: f(x)=−x3−6x2−9x
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.
Easily See Your Progress
We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.Make Use of Our Learning Aids
Earn Achievements as You Learn
Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.Create and Customize Your Avatar
Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
Topic Notes
In this section we will expand our knowledge on the connection between derivatives and the shape of a graph. By following the "5-Steps Approach", we will quantify the characteristics of the function with application of derivatives, which will enable us to sketch the graph of a function.
Guidelines for Curve Sketching
a) domain
b) Intercepts
y-intercept: set x=0 and evaluate y.
x-intercept: set y=0 and solve for x. (skip this step if the equation is difficult to solve)
c) Asymptotes
vertical asymptotes: for rational functions, vertical asymptotes can be located by equating the denominator to 0 after canceling any common factors.
horizontal asymptotes: evaluate limx→∞f(x) to determine the right-end behavior;
evaluate limx→−∞f(x) to determine the left-end behavior.
slant asymptotes: for rational functions, slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator.
d) Computef′(x)
find the critical numbers:
• use the First Derivative Test to find: intervals of increase/decrease and local extrema.
e) Computef′′(x) • inflection points occur where the direction of concavity changes.
find possible inflection points by equating thef′′(x) to 0.
•Concavity Test:
•inflection points occur where the direction of concavity changes.
2
videos
remaining today
remaining today
5
practice questions
remaining today
remaining today