Question

Examine the derivability of the following function:
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 3 minus 2 straight x comma space straight x less than 2 end cell row cell 3 straight x minus 7 comma space straight x greater or equal than 2 end cell end table close at space straight x equals 2$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

Here space straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 3 minus 2 straight x comma space straight x less than 2 end cell row cell 3 straight x minus 7 comma space straight x greater or equal than 2 end cell end table close straight L. straight H. straight D equals Lt with straight x rightwards arrow 2 to the power of minus below fraction numerator straight f left parenthesis straight x right parenthesis minus straight f left parenthesis 2 right parenthesis over denominator straight x minus 2 end fraction equals Lt with straight x rightwards arrow 2 to the power of minus below space fraction numerator left parenthesis 3 minus 2 straight x right parenthesis minus left parenthesis 6 minus 7 right parenthesis over denominator straight x minus 2 end fraction equals Lt with straight x rightwards arrow 2 to the power of minus below fraction numerator 4 minus 2 straight x over denominator straight x minus 2 end fraction space space space space space space space space space space space equals Lt with straight x rightwards arrow 2 to the power of minus below fraction numerator negative 2 left parenthesis straight x minus 2 right parenthesis over denominator straight x minus 2 end fraction equals negative 2 Lt with straight x rightwards arrow 2 to the power of minus below left parenthesis 1 right parenthesis equals left parenthesis negative 2 right parenthesis left parenthesis 1 right parenthesis equals negative 2 straight R. straight H. straight D equals Lt with straight x rightwards arrow 2 plus below fraction numerator straight f left parenthesis straight x right parenthesis minus straight f left parenthesis 2 right parenthesis over denominator straight x minus 2 end fraction equals Lt with straight x rightwards arrow 2 to the power of plus below space fraction numerator left parenthesis 3 straight x minus 7 right parenthesis minus left parenthesis 6 minus 7 right parenthesis over denominator straight x minus 2 end fraction equals Lt with straight x rightwards arrow 2 to the power of plus below fraction numerator 3 straight x minus 6 over denominator straight x minus 2 end fraction space space space space space space space space space space space stack equals Lt with straight x rightwards arrow 2 to the power of plus below fraction numerator 3 left parenthesis straight x minus 2 right parenthesis over denominator straight x minus 2 end fraction equals 3 Lt with straight x rightwards arrow 2 to the power of plus below left parenthesis 1 right parenthesis equals 3 cross times 1 equals 3 therefore space straight L. straight H. straight D not equal to straight R. straight H. straight D. therefore space straight f left parenthesis straight x right parenthesis space is space not space derivable space at space straight x equals 2.

For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location