Question

diketahui f turunan pertama (x) = x² – 4x + 1 dan f(-3) = -28, maka f(x) =

a. 1/3x³ – 2x² + x + 2
b. 1/3x³ – 2x² – x + 2
c. x³ + 2x² + x + 2
d. 3x³ – 2x² – x + 2
e. x³ – 2x² + x 2​

Answer 1

Jawaban:

a

Penjelasan dengan langkah-langkah:

f'(x) = x² - 4x + 1

f(-3) = -28

y = x² - 4x + 1

∫ (x² - 4x + 1) dx

= 1/3x³ - 1/2 . 4x² + x + c

= 1/3x³ - 2x² + x + c

f(x) = 1/3x³ - 2x² + x + c

f(-3) = 1/3(-3)³ - 2(-3)² + (-3) + c

-28 = 1/3(-27) - 18 - 3 + c

-28 = -9 - 18 - 3 + c

-28 = -30 + c

c = 30 - 28

c = 2

f(x) = 1/3x³ - 2x² + x + 2