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Question
Find the derivative of f(x) = ax2 + bx + c, where a, b and c are none-zero constant, by first principle.
Solution
By definition,
f'(x) = `lim_(h -> 0) (f(x + h) - f(x))/h`
= `lim_(h -> 0) (a(x + h)^2 + b(x + h) + c - ax^2 - bx - c)/h`
= `lim_(h -> 0) (bh + ah^2 + 2axh)/h`
= `lim_(h -> 0) ah + 2ax + b = b + 2ax`
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