Question

Tolong jwb jangan asal-asalan!​

Answer 1

f(x) = x² - 3x + 4 / (x² - x + 2)

u(x) = x² - 3x + 4

v(x) = x² - x + 2

u'(x) = 2x - 3

v'(x) = 2x - 1

f'(x)

= u'(x) . v(x) - v'(x) . u(x) / v(x)²

= (2x - 3) . (x² - x + 2) - (2x - 1) . (x² - 3x + 4) / (x² - x + 2)²

= (2x³ - 2x² + 4x - 3x² + 3x - 6) - (2x³ - 6x² + 8x - x² + 3x - 4) / (x² - x + 2)²

= (2x³ - 5x² + 7x - 6) - (2x³ - 7x² + 11x - 4) / (x² - x + 2)²

= (2x² - 4x - 2) / (x² - x + 2)

f'(2)

= (2(2)² - 4(2) - 2) / ((2)² - (2) + 2)²

= (8 - 8 - 2) / (4 - 2 + 2)²

= -2/(4²)

= -2/16

= -1/8