tolong kerjakan nomor 31 dan 32 , terimakasih :)

turunan

31.
f(x) = x³ - 7x² + 15x
f '(x) = 3x² - 14x + 15
f' (x) = (3x - 5)(x - 3)

a.
fungsi naik  f '(x) > 0 
(3x -5)(x -3) > 0 --> x > 3  atau x < 5/3

fungsi turun f '(x ) < 0
(3x -5)(x -3) < 0 --> x < 3  atau x > 5/2

b. titik stationer
f'(x)= 0
(3x-5)(x-3) =0
x = 5/3  atau x = 3
f(5/3) = 10 5/27
f(3) = 9
titik A (5/3, 10 5/27)
titk B (3,9)



Jenisnya
f'(x) = 3x² -14x + 15
f "(x) = 6x - 14

f"(5/3) = 6(5/3) - 14= -4 --> f " (5/3) < 0 --> A ttik maksimum
f"(3) = 6(3)-14 = 4 --- f"(3) > 0 , B titk minimum

32. y" =  x + 1/x³ = x + x⁻³
a. turunan pertama kurva
y' = ∫y" dx = 1/2 x² - 1/2 x⁻² + c

gradien x+2y + 4 = 0 --> m1 = -1/2
gradien garis singgung m2 = -1 /m1 = 2
m = y' = 1/2 x² -1/2 x⁻² + c  di titik x = 1
2 = 1/2(1) - 1/2(1) + c
2 = c
y'=  1/2 x² - 1/2 x⁻² + 2


c. persamaan kurva
y = ∫ y' dx
y = ∫ 1/2 x² - 1/2 x⁻² + 2 dx
y = 1/2 (1/3)x³ - 1/2 (-1)(x⁻¹) + 2x + c
y = 1/6 x³ + 1/2 x⁻¹ + 2x + c melalui ( 1,  1/3)
1/3 = 1/6(1) + 1/2 (1) + 2(1) + c
1/3 = 1/6 + 1/2 + 2 + c...kalikan 6
2 = 1 + 3 + 12 + 6c
6c = -14
c = -14/6 = - 7/3

persamaan kurva y = 1/6 x³ + 1/2 x⁻¹ + 2x - 7/3
y = ¹/₆ x³ - ¹/₍₂ₓ)  + 2x  -   ⁷/₃