Soal Matematika Kelas 11 SMA Halaman 285, 286, 287, 288 Uji Kompetensi 4.1 Fungsi Turunan

1) f(x) = 3x-2
f'(x) = 3
f”(x) = 0
2. f(x) = -2x^2 – x
f'(x) = -4x – 1

f”(x) = -4
3. f(x) = -x^4 + 2x^2 -4
f'(x) = -4x^3 + 4x
f”(x) = -12x^2 + 4
4. f(x) = (3x -2)^2
f'(x) = 2(3x-2)
= 6x-4

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f”(x) = 6
5. f(x) = 2x / x+1
u = 2x v= x+1
u’ = 2 v’= 1

f'(x) = u’v – uv’ / v^2
= 2(x+1) – 2x(1) / (x+1)^2
= (2x+2) -2x / (x+2)^2
= 2 / (x+2)^2
u = 2 v=(x+2)^2
u’ = 0 v’=2(x+2)

f”(x) = u’v – uv’ / v^2
= 0(x+2)^2 – 2(2(x+2)) / ((x+2)^2)^2
= 0 – 2(2x+2) / ((x+2)^2)^2
= – 4x + 4 / ((x+2)^2)^2

Baca Juga: Tugas Matematika Kelas 10 SMA Semester 2 Halaman 126 ,127, 128, Ukuran Sudut Derajat dan Radian

2. Tentukan titik balik fungsi-fungsi berikut!
a. f(x) = x2 – 2x
b. f(x) = – 2x² + 2/3x-3/4 /f (x) = – 1 x2 + x –
c. f(x) = x3 – x
d. f(x) = x3 – 6×2 – 9x + 1
e. f(x) = x4 – x2.

Pembahasan :

a. f(x) = x² – 2x

nilai stasioner

f ‘(x) = 0

2x – 2 = 0

x = 1