Limits and Derivatives

Limits and Derivatives

Question

Find the derivative of the function f(x) = 99x at x= 100.

Answer
space space space space space space straight f left parenthesis 100 right parenthesis space space equals space limit as straight h rightwards arrow 0 of fraction numerator straight f left parenthesis 100 plus straight h right parenthesis minus straight f left parenthesis 100 right parenthesis over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator 99 left parenthesis 100 plus straight h right parenthesis minus 99 left parenthesis 100 right parenthesis over denominator straight h end fraction

    space space space space space space space equals space limit as straight h rightwards arrow 0 of fraction numerator 99 straight h over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of 99 equals 99

 

∴ derivative of function of f(x) = 99x at x = 100 is 99.

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