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March 30, 2017

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How do I solve this using the TERM BY TERM method?

If f(x)= (2x^2 - 5x - 3) / (3-x)

find f'(-8).

  • calculus - ,

    separate the terms:

    f(x) = 2x^2/(3-x) - 5x/(3-x) - 3/(3-x)

    now use the quotient rule 3 times:

    f'(x) = -2x(x-6)/(3-x)^2 - 15/(3-x)^2 - 3/(3-x)^2

    However, this is a waste of time, since
    (2x^2 - 5x - 3) = (x-3)(2x+1)

    so, f(x) = -(2x+1)
    f'(x) = -2 as long as x≠3

    so, f'(-8) = -2

    moral: see whether a function can be simplified before delving into long calculations.

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