Question
If $f^{\prime \prime}(x)>0$ for all $x,$ then the graph of $y=f(x)$ cannot have a horizontal asymptote.
Step 1
This inequality tells us that the second derivative of the function $f(x)$ is positive for all $x$. In other words, the function $f(x)$ is concave up for all $x$. Show more…
Show all steps
Your feedback will help us improve your experience
Donald Albin and 58 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
The graph of a function can have a vertical asymptote, a horizontal asymptote, and a slant asymptote.
Polynomial and Rational Functions
Rational Functions
Can the graph of y = f(x) intersect a vertical asymptote? Yes No Can the graph of a function y = f(x) intersect a horizontal asymptote? Yes No How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.) 0 1 2 3 4
If $f$ has a vertical asymptote at $x=0,$ then $f$ is undefined at $x=0 .$
Limits and Their Properties
Infinite Limits
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD