Concavity

Tags

Calculus

Cegep/1

Word count

94 words

Reading time

1 minute

Property of a function over an interval $I$ where $\mathrm{\forall }x\in I,f^{″}(x)>0$ (up) or $f^{″}(x)<0$ (down)
2^nd degree of monotonicity

In a concave up / down function:

• Any tangent line is below / up.
• Its derivative is always increasing or decreasing.

Evaluation

To find the intervals of concavity:

1. Find the domain of $f$.
2. Find and simplify $f^{″}$.
3. Find all inflection points of $f$.
4. Construct a sign table with the inflection points.

Contributors

Ajitani Hifumi

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