Calculus

Concavity and Inflection

Where function is convex/concave

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concave down (∩)concave up (∪)Inflectionf″=1.00
x = 0.50
f(x)=x33−x,f′′(0.50)=1.000f(x)=\frac{x^3}{3}-x,\quad f''(0.50)=1.000

f″>0 → concave up (cup, tangent below curve). f″<0 → concave down (cap). Inflection point = where concavity changes (f″=0).