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29 October, 20:17

Find the different quotient f (x+h) - f (x) / h given the function of f (x) = 3x^2+2

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  1. 29 October, 22:14
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    This is 6x.

    Step-by-step explanation:

    f (x) = 3x^2 + 2

    The differential coefficient (f' (x)) is the limit as h-->0 of [ f (x+h) - f (x) ] / h.

    f' (x) = [3 (x + h) ^2 + 2 - (3x^2 + 2) ] / h

    = (3x^2 + 6hx + 3h^2 + 2 - 3x^2 - 2) / h

    = (6hx + 3h^2) / h

    = 6x + 3h

    As h approaches very close to 0 we can neglect the 3h.

    so f' (x) = 6x (answer).
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