Question

1.diket F' (x) = 6x-3x^2 dan f(0)=5 maka tentukan fungsi F(x)
2. jika f'(x) =2x+1 dan f(3)=6 tentukan fungsi f(x)​

Answer 1

Penjelasan dengan langkah-langkah:

Soal 1

[tex] \begin{aligned} f(x) &= \int (6x-3x^2) \text{ d}x \\ f(x) &= 3x^2-x^3+C \\ f(0) = 5 \;\rightarrow 5 &= 3(0)^2-0^3+C \\ 5 &= C \\ \rightarrow\; f(x) &= 3x^2-x^3+5\end{aligned} [/tex]

Soal 2

[tex] \begin{aligned} f(x) &= \int (2x+1) \text{ d}x \\ f(x)&= x^2+x+C\\ f(3)=6 \;\rightarrow\; 6 &= 3^2+3+C \\ 6 &= 9+3+C \\ 6&= 12+C \\ -6 &= C \\ \rightarrow\; f(x) &= x^2+x-6\end{aligned} [/tex]