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Question
If f(x) = x2 + 3x than show that Δf(x) = 2x + 4
Sum
Solution
Given f(x) = x3 + 3x, h = 1
Δf(x) = f(x + h) – f(x)
= (x + 1)2 + 3(x + 1) – (x2 + 3x)
= x2 + 2x + 1 + 3x + 3 – x2 + 3x
= 2x + 4
∴ Δf(x) = 2x + 4
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Finite Differences
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