Second derivatives f′′, using the sign of f′′ to determine concavity, locate inflexion points where
The derivative of the derivative of a function is its second derivative:
We determine concavity by the sign of f′′:
At a stationary point (f′(a)=0),
If f′′(a)>0, then f has a local minimum at x=a.
If f′′(a)<0, then f has a local maximum at x=a.
Using the second derivative to classify a stationary point is often called the second derivative test.
Inflexion points occur when f′′(x)=0 and f′′(x) changes sign. 🚫
When f′ crosses the x-axis f has a maximum (f′′<0) or minimum (f′′>0)
When f′′ crosses the x-axis, f has an inflexion point.
Nice work completing Second Derivatives and Applications, here's a quick recap of what we covered:
Exercises checked off
Second derivatives f′′, using the sign of f′′ to determine concavity, locate inflexion points where
The derivative of the derivative of a function is its second derivative:
We determine concavity by the sign of f′′:
At a stationary point (f′(a)=0),
If f′′(a)>0, then f has a local minimum at x=a.
If f′′(a)<0, then f has a local maximum at x=a.
Using the second derivative to classify a stationary point is often called the second derivative test.
Inflexion points occur when f′′(x)=0 and f′′(x) changes sign. 🚫
When f′ crosses the x-axis f has a maximum (f′′<0) or minimum (f′′>0)
When f′′ crosses the x-axis, f has an inflexion point.
Nice work completing Second Derivatives and Applications, here's a quick recap of what we covered:
Exercises checked off