WAEC 2019 · Paper 2 · Q2

Differentiation

(a)
Differentiate from first principles, with respect to $x$ , $(3x^2 + 2x - 1)$ .

Worked solution (try it first)

$f(x + h) = 3(x + h)^2 + 2(x + h) - 1$
$= 3x^2 + 6xh + 3h^2 + 2x + 2h - 1$ .
Take away $f(x) = 3x^2 + 2x - 1$ : $f(x + h) - f(x) = 6xh + 3h^2 + 2h$ .
Divide by $h$ : $6x + 3h + 2$ .
Let $h \to 0$ : $f'(x) = 6x + 2$ .

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