Question

Tentukan rumus fungsi f ( x )jika di ketahui :
A. F' (x) = 4x + 3 dan f (- 1 ) = 5
B.F' (x) = 6 - 4x + 7 dan f (2) + 5

Answer 1

F(x)= ∫ F'(x) dx
a) f(x) = ∫4x+3 dx = 2x² + 3x + c
f(-1) = 5
2- 3 + c = 5
c = 6
f(x) = 2x² + 3x + 6

b)  f(x) = ∫ 6x² - 4x + 7 dx
f(x) = 2x³ - 2x² + 7x + c
f(2)= 5
2(2)³ - 2 (2)² +7(2) + c = 5
16 - 8 + 14 + c = 5
22 + c = 5
x = 5 - 22
c = -17
f(x) = 2x³ - 2x² + 7x - 17

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