Diketahui f'(x)=6x²-2x+4 dan f(-1)=-10, maka f(x)=... A. 12x³-x²+4x-2 B. 12x³-x²+4x+8 C. 2x³-x²+4x-10 D. 2x³-x²+4x-3 E. 2x³-x²+4x-4

Materi : Persamaan Diferensial Sederhana
Kelas : Xll Sma

Soal
Dik : f'(x) = 6x² - 2x + 4
f(-1)=-10
Dit : f(x)

Penyelesaian
f(x) = integral f'(x) dx
f(x) = integral (6x² - 2x + 4) dx
f(x) = 6x³/3 - 2x²/2 + 4x + c
f(x) = 2x³ - x² + 4x + c

f(-1) = 2(-1)³ - (-1)² + 4(-1) + c = -10
-2 - 1 - 4 + c = -10
-7 + c = -10
c = -10 + 7
c = -3

Maka f(x) = 2x³ - x² + 4x - 3 (D)