Question 1111998: HELPP! Using the Δ definition, show that the derivative of any linear function f(x) = Ax +B is f'(x) = A.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the definition of derivation is f'(x) = limit of (f(x+h) - f(x)) / h, as h approaches 0.
when f(x) = Ax + B, this becomes:
f'(x) = limit of (A(x+h) - B - (Ax + B) / h, as h approaches 0, which becomes:
f'(x) = limit of (Ax + Ah - B - Ax = B) / h, as h approaches 0.
Ax - Ax cancels out and B - B cancels out, so you are left with:
f'(x) = limit of Ah / h, as h approaches 0.
as long as h approaches 0, but is never 0, then h cancels out and you are left with:
f'(x) = A.
here's a reference on derivative of a function.
http://web.mit.edu/wwmath/calculus/differentiation/definition.html
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