Question

Tolong bantuannya kakak kakak. trims.

Answer 1

1) f(x) = x 3√x + 2x^2 - 6x = x . x^(1/3) + 2x^2 - 6x = x^(4/3) + 2x^2 - 6x
f'(x) = (4/3) x^(1/3) + 4x - 6
f'(27) = (4/3) (27)^(1/3) + 4(27) - 6 = (4/3) . 3 + 108 - 6 = 4 + 102 = 106

2) f(x) = 2x^3 - 9x^2 + 12x , naik jika f'(x) > 0
f'(x) = 6x^2 - 18x + 12 > 0
=> x^2 - 3x + 2 > 0
=> (x - 1)(x - 2) > 0
=> x = 1 atau x = 2
Buat garis bilangan
+++ (1) --- (2) +++ => ambil daerah yg positif
x < 1 atau x > 2

3) int (x^2 + x - 2) dx
= (1/3)x^3 + (1/2) x^2 - 2x |
= [(1/3).2^3 + (1/2) . 2^2 - 2(2)] - [(1/3) . (-1)^3 + (1/2) (-1)^2 - 2(-1)]
= [8/3 + 2 - 4] - [-1/3 + 1/2 + 2]
= 8/3 - (-1/3) + 2 - 4 - 1/2 - 2
= 9/3 - 4 - 1/2
= 3 - 4 - 1/2
= -1 1/2..... c