turunan pertama dan kedua fungsi f berturut turut f'dan f'' jika f''(x)=12x²+4, f'(1)=8 , f(1)=4 tentukan rumus fungsinya

integral

f" (x)= 12 x² + 4
f '(1) = 8
f(1)= 4
.

f '(x)= ∫ f'(x) dx
f '(x) = ∫12x² + 4 dx
f '(x) = 4x³ + 4x + c
f ' (1) =8 --> 4(1)³ + 4(1) + c= 8
4+4+ c = 8
c= 0

f'(x) = 4x³ + 4x
f (x) = ∫ f'(x) dx
f (x) =x⁴ + 2x² + c
f (1)= 4 --> 1⁴ + 2.1² + c = 4
1 + 2 + c = 4
c = 1

f(x) =x⁴+ 2x² + 1