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18 November, 23:17

Suppose that f (x+h) - f (x) = - 6hx2-7hx-6h2x-7h2+2h3.

Find f′ (x).

f′ (x) =

+1
Answers (1)
  1. 19 November, 01:57
    0
    By definition,

    f' (x) = Lim h->0 (f (x+h) - f (x)) / h

    We are already given

    f (x+h) - f (x) = - 6hx2-7hx-6h2x-7h2+2h3=h (-6x^2-7x-6hx-7h+2h^2)

    divide by h

    (f (x+h) - f (x)) / h = h (-6x^2-7x-6hx-7h+2h^2) / h = (-6x^2-7x-6hx-7h+2h^2)

    Finally, take lim h->0

    f' (x) = Lim h->0 (f (x+h) - f (x)) / h = (-6x^2-7x-0-0+0) = - 6x^2-7x

    =>

    f' (x) = - 6x^2-7x
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