Question

Tolong dong no 1 yg c, d, e dengan caranya

Answer 1

C. f(x) = x^2 (x + 4) = x^3 + 4x^2
=> f'(x) = 3x^2 + 8x
=> x(3x + 8) = 0
=> x = 0 atau x = -8/3
garis bilangan
+++ (-8/3) --- (0) +++
fungsi naik : x < -8/3 atau x > 0
fungsi turun : -8/3 < x < 0

d. f(x) = (x^2 - 8)/(x - 3)
u = x^2 - 8 => u' = 2x
v = x - 3 => v' = 1
f'(x) = (u'v - v'u)/v^2
= (2x(x - 3) - 1(x^2 - 8))/(x - 3)^2
= (2x^2 - 6x - x^2 + 8)/(x - 3)^2
= (x^2 - 6x + 8)/(x - 3)^2
= (x - 4)(x - 2)/(x - 3)^2
x = 4 atau x = 2 atau x = 3
garis bilangan
+++ (2) --- (3) --- (4) +++
fungsi naik : x < 2 atau x > 4
fungsi turun : 2 < x < 3 atau 3 < x < 4
= 2 < x < 4, x ≠ 3

e. f(x) = (x - 2)/(x^2 + x - 2)
u = x - 2 => u' = 1
v = x^2 + x - 2 => v' = 2x + 1
f'(x) = (u'v - v'u)/v^2
= (1(x^2 + x - 2) - (2x + 1)(x - 2))/(x^2 + x - 2)^2
= (x^2 + x - 2 - (2x^2 - 3x - 2)) / (x^2 + x - 2)^2
= (-x^2 + 4x) / (x^2 + x - 2)^2
= -x (x - 4) / ((x + 2)(x - 1))^2
x = 0 atau x = 4 atau x = -2 atau x = 1
garis bilangan
--- (-2) --- (0) +++ (1) +++ (4) ---
fungsi naik : 0 < x < 1 atau 1 < x < 4
= 0 < x < 4, x ≠ 1
fungsi turun: x < -2 atau -2 < x < 0 atau x > 4
= x < 0 atau x > 4, x ≠ -2