Quiz (+50):, #QuizYangTidakUmum, Interval turun fungsi, f(x) = \xbd(x\xb3) + \xbc(x\xb2) – x + C, adalah a > x > b, Buktikan jika nilai a – b = 12154

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Quiz (+50):


#QuizYangTidakUmum

Interval turun fungsi
f(x) = ½(x³) + ¼(x²) – x + C
adalah a > x >

Buktikan jika nilai a – b = 1⅔

Jawaban:

Anti turunan fungsi

f(x) = ½x³ + ¼ (x²) – x + C

f(x) = 3(½)x³-¹ + 2(¼)x²-¹ – 1

f(x) = 3/2x² + ½x – 1

syarat interval fungsi turun f(x) < 0

maka,

3/2x² + 1/2x – 1 < f(x)

3/2x² + 1/2x – 1 < 0 .. kali ruas dengan ( x 2 )

3x² + x – 2 < 0

(x + 1)(3x – 2) < 0

x1 = -1 V x2 = 2/3

a > x > b

2/3 > x > -1

..

= a – b

= 2/3 – (-1)

= 2/3 + 1

= (2 + 3)/3

= 5/3

= 1 ⅔

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