Question

Jika m dan n bilangan real dan fungsi (x) = mx³ + 2x² - nx + 5 memenuhi f'(1) = f'(-5) = 0, nilai 3m + n adalah...

Diharap tdk menjawab asal. Terimakasih^^

[tex] \: \: [/tex]
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Answer 1

Nilai 3m + n
= 6

Penjelasan:
Diketahui
f(x) = mx³ + 2x² - nx + 5
memenuhi f'(1) = f'(-5) = 0,
Ditanya nilai 3m + n
------------------------------------
f(x) = mx³ + 2x² - nx + 5
f'(x) = (3m)x³⁻¹ + 2(2)x²⁻¹ - n
f'(x) = (3m)x² + 4x - n
bila memenuhi f'(1) = f'(-5) = 0
f'(1) = 0
0 = (3m)(1)² + 4(1) - n
n = 3m + 4
f'(-5) = 0
0 = (3m)(-5)² + 4(-5) - n
0 = 25(3m) - 20 - n
n = 75m - 20
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Samakan untuk mencari m
3m + 4 = 75m - 20
75m - 3m = 4 + 20
72m = 24
m = ²⁴/₇₂ : (²⁴/₂₄)
m = ¹/₃ ←
------------------------------------
Lalu cari n dgn salah satu pers.
n = 3m + 4
n = 3(¹/₃) + 4
n = 1 + 4
n = 5 ←
------------------------------------
Nilai 3m + n =
3(¹/₃) + 5 =
1 + 5 =

6