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elementary functions

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f(x)=x(squared)+x-3. compute the difference quotient: (f(x+h)-f(x))/h

  • elementary functions -

    f(x+h) = (x+h)^2 + x+h - 3
    = x^2 + 2xh + h^2 + x + h - 3

    then ( f(x+h) - f(x) )/h
    = (x^2 + 2xh + h^2 + x +h - 3 - x^2 - x + 3)/h
    = ( 2xh + h^2 +h)/h
    = h(2x + h + 1)/h
    = 2x + h + 1 , h ≠0

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