Understanding Critical Values of a Function

[tandoorichicken]

What is the definition of a critical value of a function?

 

[hitssquad]

Main Entry: critical value
Function: noun

mathematics : the value of the argument or independent variable corresponding to a critical point of a function

 

[hitssquad]

Main Entry: critical point
Function: noun

1 mathematics : a point on the graph of a function where the derivative of the function is zero or infinite
2 : TRANSFORMATION TEMPERATURE
3 a : the point on a phase diagram of a pure substance that corresponds to its critical state b : CRITICAL STATE

 

[st3dent]

The critical point on a graph is a point where:

1) The derivative of f is equal to zero.
2) The derivative of f does not exist.

 

[HallsofIvy]

Main Entry: critical point
Function: noun

1 mathematics : a point on the graph of a function where the derivative of the function is zero or infinite
2 : TRANSFORMATION TEMPERATURE
3 a : the point on a phase diagram of a pure substance that corresponds to its critical state b : CRITICAL STATE

Did you really copy this correctly? A critical point of a function is one where the derivative is zero or does not exist. That does not necessarily mean "is infinite". The absolute value function f(x)= |x| has a critical point at x=0.