Jika turunan pertama suatu fungsi f'(x) =(2x +4)^2 f(1)= 34 berapah kah f(X) nYa.... Question from @prastiyonoe

October 2018 2 37 Report

Jika turunan pertama suatu fungsi
f'(x) =(2x +4)^2
f(1)= 34
berapah kah f(X) nYa

Kilos F'(x) = (2x + 4)²
f'(x) = 4x² + 16x + 16

f(x) = 4/3x³ + 8x² + 16x + c

f(1) = 34
4/3(1)³ + 8(1)² + 16(1) + c = 34
4/3 + 8 + 16 + c = 34
4/3 + 24 + c = 34
4/3 + c = 14
c = 14 - 4/3
c = 42-4 / 3
c = 38/3

f(x) = 4/3x³ + 8x² + 16x + 38/3

0 votes Thanks 2

izharulhaq78 $f'(x)=(2x+4)^2 \\ f'(x)=4x^2+16x+16 \\ \\ f(x)= \frac{4}{3}x^{2+1}+ \frac{16}{2}x^2 + \frac{16}{1}x^1+c \\ f(x)= \frac{4}{3}x^{3}+ 8x^2 + 16x+c \\ \\ f(1)=34 \\ \frac{4}{3}(1)^{3}+ 8(1)^2 + 16(1)+c=34 \\ \frac{4}{3}+ 8 + 16+c=34 \\ \frac{4}{3}+ 24+c=34 \\ \frac{4}{3}+c=34-24 \\ \frac{4}{3}+c=10 \\ c=10-\frac{4}{3} \\ c= \frac{30}{3} -\frac{4}{3} \\ c=\frac{26}{3} \\ c=8 \frac{2}{3} \\ \\f(x)= \frac{4}{3}x^{3} + 8x^2 + 16x+8 \frac{2}{3}$

Maaf kalau salah

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