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10 votes
10 votes
F ( x ) = − x 2 − x . compute f ( a h ) − f ( a ) = assuming h ≠ 0 , compute f ( a h ) − f ( a ) h

User Bytejunkie
by
2.9k points

1 Answer

15 votes
15 votes

Given


f(x) = -x^2 - x

we have


f(a) = -a^2 - a


f(a+h) = -(a+h)^2 - (a+h) = -a^2 - 2ah - h^2 - a - h


\implies f(a+h) - f(a) = (-a^2 - 2ah - h^2 - a - h) - (-a^2 - a) = -2ah - h^2 - h


\implies \frac{f(a+h) - f(a)}h = \boxed{-2a - h - 1}

User Ryenski
by
2.9k points
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