Matematika Tentukan interval agar setiap fungsi berikut naik!A. [tex]f(x) = - {x }^{2} - 4x + 1[/tex]B. [tex]f(x) = {x}^{3} + 3 {x}^{2} - 9x - 4[/tex]MOHON BANTUANNYA YAA!​

dylangaylordulv – June 04, 2023

Tentukan interval agar setiap fungsi berikut naik!
A.
[tex]f(x) = - {x }^{2} - 4x + 1[/tex]
B.
[tex]f(x) = {x}^{3} + 3 {x}^{2} - 9x - 4[/tex]

MOHON BANTUANNYA YAA!​

f(x) = -x² - 4x + 1

= 2.-1 x^(2-1) - 1.4 x^(1-1) + 0

= -2x² - 4x⁰

= -2x - 4

f'(x) > 0

-2x - 4 > 0

-4 > 2x

HP : {x | x < -2}

B.

f(x) = x³ + 3x² - 9x - 4

= 3.1 x^(3-1) + 2.3 x^(2-1) - 1.9 x^(1-1)

= 3x² + 6x¹ - 9x⁰

= 3x² + 6x - 9

3x² + 6x - 9 > 0

x² + 2x - 3 > 0

(x + 3) (x - 1) > 0

x = -3 V x = 1

x = -4 => (-4 + 3)(-4 - 1) = 5

x = 0 => (0 + 3)(0 - 1) = -3

x = 2 => (2 + 3)(2 - 1) = 5

HP : {x | x < -3 dan x > 1}

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