# Second Derivatives and Beyond

### Terms

### Concavity

The concavity of a function describes whether the function is curving up, down or not curving at all.### Critical Point

The derivative of the function at the critical point is 0.### Inflection Point

The point (*x*-value) where the function changes concavity.

### Implicit Differentiation

Differentiation of an equation in which the dependent variable doesn't have a side of the equation all to itself.### Derivative Of A Function

The derivative of*f*(

*x*) measures how

*f*(

*x*) changes at a point

*x*.

### Minima

The largest value that a function takes within a given interval.### Maxima

The smallest value that a function takes within a given interval.### Local Extreme Point

The maximum and minimum points when the domain is restricted to a small neighborhood of*x*â€“values.

### Global Extreme Point

The maximum and minimum points in the entire domain of the function.### Instantaneous Rate Of Change

Change in the function*f*(

*x*) at a point

*x*.

### Secant Line

Line joining two points on the graph of a function.### Tangent Line

A line that touches the graph of a function*f*(

*x*) at a point.

### Differentiability

If the limit exists, the function*f*(

*x*) is differentiable at

*x*=

*a*.

Advertisement

Advertisement

Advertisement