explain how to find the critical numbers of a function.\nto find the critical numbers of ( f ), determine…

explain how to find the critical numbers of a function.\nto find the critical numbers of ( f ), determine all values of ( x ) where which of the following are true? (select all that apply.)\n( square f^{prime}(x) ) does not exist\n( square f(x)=f^{prime}(x) )\n( square f(x)=0 )\n( square x = 0 )\n( square f^{prime}(x)=0 )

explain how to find the critical numbers of a function.\nto find the critical numbers of ( f ), determine all values of ( x ) where which of the following are true? (select all that apply.)\n( square f^{prime}(x) ) does not exist\n( square f(x)=f^{prime}(x) )\n( square f(x)=0 )\n( square x = 0 )\n( square f^{prime}(x)=0 )

Answer

Brief Explanations:

Critical numbers of a function ( f(x) ) are values of ( x ) in the domain of ( f ) where either ( f^{\prime}(x)=0 ) (the derivative is zero, indicating a possible local maximum, minimum, or inflection point) or ( f^{\prime}(x) ) does not exist (such as at points of discontinuity, corner - points, or vertical tangents in the graph of the function).

  • For ( f(x)=f^{\prime}(x) ), this is not a standard condition for critical numbers. For example, if ( f(x)=e^{x} ), ( f(x) = f^{\prime}(x)), but this is just a property of the exponential function and not a general rule for critical numbers.
  • ( f(x) = 0 ) gives the ( x ) - intercepts of the function ( y = f(x)), not the critical numbers.
  • ( x = 0 ) is just a specific value of ( x) and not a general condition for critical numbers.

Answer:

  • ( f^{\prime}(x)) does not exist
  • ( f^{\prime}(x)=0)