MATEMATIKA INDONESIA

Selasa, 02 Oktober 2012

Soal-Soal Fungsi Kuadrat

Berikut ini adalah soal-soal fungsi kuadrat

1. Jika f(x) = x² - 6x + 10 maka sumbu simetri dari f(x) adalah ...

Jawab :
Sumbu simetri

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2. Fungsi f(x) = -x² + 8x + 1 mengalami maksimum pada saat x = ...

Jawab :
Nilai maksimum terjadi pada sumbu simetri, jadi yang ditanyakan soal adalah sumbu simetrinya
maka
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3. Nilai minimum dari fungsi f(x) = x² - 4x + 8 adalah

Jawab :

Nilai minimum didapat dari

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Cara II

hasil ini tinggal kita substitusikan ke f(x) sehingga
y = f(2) = 2² - 4.2 + 8 = 4 - 8 + 8 =4

4. Jika fungsi f(x) = -2x² + 12x + 15 maka nilai maksimumnya adalah ....

Jawab :
Nilai maksimum adalah
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Cara II
kita cari nilai x nya dulu

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Nilai maksimunya adalah
y = f(-3) = -2.3² + 12.3 + 15 = -18 + 36 + 15 = 33

5. Fungsi f(x) = -3x² + (p+2) x + 9 memiliki sumbu simetri x = 2. Nilai p sama dengan ...

Jawab :
sumbu simetri
x = 2

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p + 2 = 12
p = 10

6. Agar fungsi f(x) = 2x² - (k-1)x + 14 memiliki nilai minimum untuk x = 5 maka nilai k sama dengan ...

Jawab :
Nilai minimum terjadi pada sumbu simetri

x = 5

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k - 1 = 20
k = 21

(tunggu lanjutannya ya)

Rumus-Rumus Turunan

Dari definisi turunan

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maka diperoleh rumus-rumus turunan fungsi sebagai berikut :

f(x) = c ===> f'(x) = 0
f(x) =xⁿ ===> f '(x) = nx^n-1
f(x) = sin x ===> f '(x) = cos x
f(x) = cos x ===> f '(x) = - sin x
f(x) = tan x ===> f '(x) = sec² x
f(x) = cot x ===> f '(x) = - csc² x
f(x) = sec x ===> f '(x) = sec x tan x
f(x) = csc x ===> f '(x) = -csc x cot x
f(x) = e^x ===> f'(x) = e^x
f(x) = ln x ===> f'(x) = 1/x
f(x) = a^x ===> f'(x) = a^x ln a
f(x) = ^alog x ===> f(x) = 1/(x ln a)

untuk fungsi e^x , ln x, a^x, ^alog x, penurunanya ada di bilangan natural.

Contoh 1 :
Turunan pertama dari f(x) = x⁵ + 6x² - 8x - 7 adalah ....

Jawab :
f(x) = x⁵ + 6x² - 8x¹ - 7
f '(x) = 5x^5-1 + 2.6x^2-1 - 1.8x⁰ + 0
f '(x) = 5x⁴ + 12x - 8

Contoh 2 :
Jika f(x) = (2x + 5)² maka f '(x) = ...

Jawab :
f(x) = (2x)² + 2.2x.5 + 5² = 4x² + 20x¹ + 25

f '(x) = 2.4x^2-1 +1.20x^1-1+ 0 = 8x + 20

Contoh 3 :
Tentukan turunan pertama dari
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Jawab :
f(x) = 5x^-3 - 3x^-1
f '(x) = -3.5x^-3-1 - (-1)3x^-1-1 = -15x^-4 + 3x^-2
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Contoh 4 :
Turunan pertama dari
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adalah ....

Jawab :
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Contoh 5 :
Tentukan turunan pertama dari
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Jawab :

Contoh 6 :
Turunan dari
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adalah ...

Jawab :
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Contoh 7 :
Jika
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maka f '(x) = ...

Jawab :
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Berlanjut ke sifat-sifat turunan

Untuk melihat meteri-materi sebelumnya, silakan klik di
Turunan

Turunan 2
Turunan 3
Turunan 4
Turunan 5
Turunan Trigonometri

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