TURUNAN FUNGSI ALJABAR

mungkin yang dimaksud :

f(x) = (x² + 3x -3)(x² -5x + 4)(x² -4x + 5)

misal : f(x) = u.v maka :

u = x² + 3x -3

u' = 2x + 3

v = (x² -5x + 4)(x² -4x + 5)

misal v = a.b maka :

a = x² -5x + 4

a' = 2x -5

b = x² -4x + 5

b' = 2x -4

maka :

v' = a'b + ab'

= (2x -5)(x² -4x + 5) + (x² -5x + 4)(2x -4)

= 2x³ -13x² + 30x -25 + 2x³ -14x² + 28x -16

= 4x³ -27x² + 58x -41

maka :

f'(x) = u'v + uv'

= (2x + 3)(x² -5x + 4)(x² -4x + 5) + (x² + 3x -3)(4x³ -27x² + 58x -41)

f'(1) = (2(1) + 3)(1² -5(1) + 4)(1² -4(1) + 5) + (1² + 3(1) -3)(4(1)³ -27(1)² + 58(1) -41)

f'(1) = (5 × 0 × 2) + (1 × (-6))

f'(1) = -6

[Opsi C]