A function f is defined as Show that f is not differentiable at
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    Continuity and Differentiability

    Multiple Choice QuestionsShort Answer Type

    131. Prove that the greatest integer function [x] is not differentiable at x = 1.
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    132. Prove that the function f given by f(x) = |x - 1 |, x ∈ R is not differentiable at x = 1.
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    133. Prove space that space straight f left parenthesis straight x right parenthesis equals open vertical bar straight x minus 3 close vertical bar space has space no space derivative space at space straight x equals 3.
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    134. If space straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x space sin 1 over straight x comma space space space straight x not equal to 0 end cell row cell 0 space space space space space space space space space comma space space space straight x equals 0 end cell end table close the space show space that space straight f space is space not space differentiable space at space straight x equals 0.
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    135. Syntax error from line 1 column 169 to line 1 column 176.
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    136. Examine the derivability of the following functions :
    |x| at x = 0
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    137. Examine the derivability of the following functions :
    |x2| at x = 0
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    138. A function f is defined as straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 1 plus straight x comma space if space straight x less or equal than 2 end cell row cell 5 minus straight x comma space if space straight x greater than 2 end cell end table closeShow that f is not differentiable at x = 2.

    Here space straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 1 plus straight x comma space if space straight x less or equal than 2 end cell row cell 5 minus straight x comma space if space straight x greater 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 fraction numerator left parenthesis 1 plus straight x right parenthesis minus 3 over denominator straight x minus 2 end fraction space space space space space space space space space space space left square bracket because space straight f left parenthesis 2 right parenthesis equals 1 plus 2 equals 3 right square bracket space space space space space space space space space space space space space space space space space space space space space space space 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 straight x minus 2 over denominator straight x minus 2 end fraction equals 1 straight R. straight H. straight D equals Lt with straight x rightwards arrow 2 to the power of 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 fraction numerator left parenthesis 5 minus straight x right parenthesis minus 3 over denominator straight x minus 2 end fraction equals Lt with straight x rightwards arrow 2 to the power of plus below fraction numerator 2 minus straight x over denominator straight x minus 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals Lt with straight x rightwards arrow 2 to the power of plus below fraction numerator negative left parenthesis straight x plus 2 right parenthesis over denominator straight x minus 2 end fraction equals negative 1 therefore space space straight L. straight H. straight D not equal to straight R. straight H. straight D therefore space straight f space is space not space derivable space at space straight x equals 2.
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    139. 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 straight x squared space sin 1 over straight x comma space straight x not equal to 0 end cell row cell space space space space space space space 0 space space space comma space space space space straight x equals 0 end cell end table close
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    140. 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
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