Limits and Derivatives

Limits and Derivatives

Question

Find the derivative of x2-2 at x = 10.

Answer

Let  f(x)  = x2-2
Now, f (10) denote the derivative of x2-2 at x = 10.

∴    f' (10) space space space space space space space space space space space space space space space space space space space space space space equals limit as straight h rightwards arrow 0 of fraction numerator straight f left parenthesis 10 plus straight h right parenthesis minus straight f left parenthesis 10 right parenthesis over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator left square bracket 10 plus straight h right square bracket squared minus 2 right square bracket minus left parenthesis left parenthesis 10 right parenthesis squared minus 2 right square bracket over denominator straight h end fraction

               space space space space space space space space space space space space space space space equals space limit as straight h rightwards arrow 0 of fraction numerator 100 plus straight h squared minus 20 straight h minus 2 minus 100 plus 2 over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator straight h squared plus 20 straight h over denominator straight h end fraction
                      space space space space space space space equals space space space limit as straight h rightwards arrow 0 of left parenthesis straight h plus 20 right parenthesis equals 0 plus 20
Hence, f(10)=20

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