Question

Buatlah sebuah soal matematika rumit, tapi singkat dan berhasilkan 13
(Bukan soal cerita)​

Answer 1

بِسْـــــــمِ اللّٰهِ الرَّحْمٰنِ الرَّحِيْمِ

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Soal:

Jika f(x) = x² + 7x + 12, tentukan f'(3).

Jawaban:

[tex]\begin{aligned}f'(a) &= \lim_{x \to a} ~ \frac{f(x) - f(a)}{x - a} \\f'(3) &= \lim_{x \to3} ~ \frac{f(x) - f(3) }{x - 3} \\ &= \lim_{x \to3} ~ \frac{ {x}^{2} + 7x + 12 - ( {3}^{2} + 7(3) + 12) }{x - 3} \\&= \lim_{x \to3} ~ \frac{ {x}^{2} + 7x + 12 - 42 }{x - 3} \\&= \lim_{x \to3} ~ \frac{ {x}^{2} + 7x - 30 }{x - 3} \\&= \lim_{x \to3} ~ \frac{ \bcancel{(x - 3)}(x + 10)}{ \bcancel{x - 3}} \\&= \lim_{x \to3} ~x + 10 \\ &=3 + 10 \\&=13 \end{aligned}[/tex]

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وَاللّٰهُ اَعْلَمُ بِاالصَّوَافَ