f(x) = 10x⁴ + 5x⁵ - 2022
f"(3) = ...*
⇲ Rules :
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Semoga aja si dia baca gambar nya :)
Penjelasan dengan langkah-langkah:
[tex] \rm f(x) = 10 {x}^{4} + 5x {}^{5} - 2022[/tex]
ditanya
f''(3)
jawab
[tex] \rm f(x) = 10 {x}^{4} + 5x {}^{5} - 2022[/tex]
[tex] \rm f'(x) = 4.10 {x}^{4 - 1} + 5.5{x}^{5 - 1} - 0[/tex]
[tex] \rm f'(x) = 40 {x}^{3} + 25{x}^{4} [/tex]
[tex] \rm f''(x) = 3.40 {x}^{3 - 1} +4 . 25{x}^{4 - 1} [/tex]
[tex] \rm f''(x) = 120 {x}^{2} +100{x}^{3} [/tex]
[tex]_________________[/tex]
menentukan f''(3)
[tex] \rm f''(x) = 120 {x}^{2} +100{x}^{3} [/tex]
[tex] \rm f''(3) = 120 ({3}^{2} ) +100({3}^{3} )[/tex]
[tex] \rm f''(3) = 120 (9) +100(27 )[/tex]
[tex] \rm f''(3) = 1.080+2.700[/tex]
[tex] \rm f''(3) = 3.780[/tex]
penyelesaian :
----------------------------------------------
f(x) = axⁿ
f'(x) = n.axⁿ-¹
=============
mencari turunan pertama
f(x) = 10x⁴ + 5x⁵ - 2022
f'(x) = 4.10x⁴-¹ + 5.5x⁵-¹ - 0
f'(x) = 40x³ + 25x⁴
mencari turunan kedua
f'(x) = 40x³ + 25x⁴
f''(x) = 3.40x³-¹ + 4.25x⁴-¹
f"(x) = 120x² + 100x³
subtitusi
f(x) = 120x² + 100x³
f(3) = 120(3)² + 100(3)³
f(3) = 120(9) + 100(27)
f(3) = 1.080 + 2.700
f(3) = 3.780
[answer.2.content]
