[b]uStationary points[/u]/b

Stationary points occur when (\dfrac{dy}{dx}=0). The second derivative can be used to test whether the stationary point is a maximum or a minimuum.
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[col]pMaximum points have (\dfrac{dy}{dx}=0) and (\dfrac{d^2y}{dx2} < 0).[/p]mtaimg/images/topics/7/7-77-1.png[/mtaimg]/col
[col]pMinimum points have (\dfrac{dy}{dx}=0) and (\dfrac{d^2y}{dx2} > 0).[/p]mtaimg/images/topics/7/7-77-2.png[/mtaimg]/col
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[b]uPoints of inflection[/u]/b

Points of inflection occur when (\dfrac{d^2y}{dx2} = 0). Points of inflections can be stationary or non-stationary.
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[col]pStationary points of inflection have (\dfrac{dy}{dx}=0) and (\dfrac{d^2y}{dx2} = 0).[/p]mtaimg/images/topics/7/7-77-3.png[/mtaimg]/col
[col]pNon-stationary points of inflection have (\dfrac{dy}{dx} \neq 0) and (\dfrac{d^2y}{dx2} = 0).[/p]mtaimg/images/topics/7/7-77-4.png[/mtaimg]/col
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[b]uDecreasing or increasing functions[/u]/b

Sections of curves can be bdecreasing/b or bincreasing/b.
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[col][p]color=redDecreasing/color sections of curves have (\dfrac{dy}{dx} < 0).[/p]mtaimg/images/topics/7/7-77-7.png[/mtaimg]/col
[col][p]color=greenIncreasing/color sections of curves have (\dfrac{dy}{dx} > 0).[/p]mtaimg/images/topics/7/7-77-8.png[/mtaimg]/col
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[b]uConcave or convex[/u]/b

Sections of curves can be bconcave/b (n-shaped, imagine the entrance of a cave) or bconvex/b (u-shaped).
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[col][p]color=redConcave/color sections of curves have (\dfrac{d^2y}{dx2} < 0).[/p]mtaimg/images/topics/7/7-77-5.png[/mtaimg]/col
[col][p]color=greenConvex/color sections of curves have (\dfrac{d^2y}{dx2} > 0).[/p]mtaimg/images/topics/7/7-77-6.png[/mtaimg]/col
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Stationary points occur when (\dfrac{dy}{dx}=0).

Maximum points have (\dfrac{dy}{dx}=0) and (\dfrac{d^2y}{dx2} < 0).

Minimum points have (\dfrac{dy}{dx}=0) and (\dfrac{d^2y}{dx2} > 0).

Stationary points of inflection have (\dfrac{dy}{dx}=0) and (\dfrac{d^2y}{dx2} = 0).

Non-stationary points of inflection have (\dfrac{dy}{dx} \neq 0) and (\dfrac{d^2y}{dx2} = 0).

Decreasing sections of curves have (\dfrac{dy}{dx} < 0) and increasing sections of curves have (\dfrac{dy}{dx} > 0).

Concave sections of curves have (\dfrac{d^2y}{dx2} < 0) and convex sections of curves have (\dfrac{d^2y}{dx^2} > 0).