Question
Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points.$$f(x)=\frac{1}{1+x^{2}}$$
Step 1
The function is $f(x)=\frac{1}{1+x^{2}}$. Using the quotient rule, we get: $$f'(x)=-\frac{2x}{(1+x^{2})^{2}}$$ Show more…
Show all steps
Your feedback will help us improve your experience
Rakesh Kumar Sharma and 61 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Concavity Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. $$f(x)=\frac{1}{1+x^{2}}$$
Applications of the Derivative
What Derivatives Tell Us
Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. $$f(x)=x^{4}-2 x^{3}+1$$
Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. $$f(x)=e^{-x^{2} / 2}$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD