Concave Up and Down Functions, and Inflection Points
Read this topicExplanations 2
- The concavity of a function/graph is an important property pertaining to the second derivative of the function. In particular: If f′′(x)>0f''(x) > 0f′′(x)>0, the graph is concav…
By Joshua Siktar, Moor Xu, Victor Wang, Joshua Siktar
- (Video) Concavity, Inflection Points, and Second Derivatives by PatrickJMT Here's a video by patrickJMT showing you how the second derivative test can tell us the concavity of a…
By Alex Federspiel, Joshua Siktar
Problems 21
- Classify the concavity of f(x)=x3−5x2f(x) = x^3 - 5x^2f(x)=x3−5x2 at x=1x=1x=1.
- Is the function described in the table above concave up or concave down?
- Using the graph above of the function f(x)=x3−6x2−15x+20f(x)=x^3-6x^2-15x+20f(x)=x3−6x2−15x+20, estimate the intervals on which the function is concave up and concave down.
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- Does the table represent a function that is increasing or decreasing? Is it concave up or concave down?
- When is the function graphed above concave up? Concave down?
- When is the function graphed above concave up? Concave down?
- When is the function graphed above concave up? Concave down?
- When is the function graphed above concave up? Concave down?
- Find the inflection point(s) of f(x)=2x3−24x2+5x+3f(x)=2x^3-24x^2+5x+3f(x)=2x3−24x2+5x+3
- Find where the equation is concave upward and downward f(x)=2x3−24x2+5x+3f\left(x\right)=2x^3-24x^2+5x+3f(x)=2x3−24x2+5x+3
- Does the table above show a function that is convex or concave?
- We've all heard someone say, "It's hot enough to fry an egg on the sidewalk" on a particular hot day, but have we ever stopped to think if that was possible? One of these buildi…
- Which of the following functions are convex on one portion of the real line and concave on the other portion?
- Does the table above show a function that has an increasing or decreasing slope?