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Question
If f” (x) = 12x – 6 and f(1) = 30, f’(1) = 5, find f(x)
Solution
f'(x) = – 6x + c
f'(x) = 6x2 – 6x + c
But f'(1) = 5
6(1)2 – 6(1) + c = 5
c = 5
f”(x) = 6x2 – 6x + 5
`int f"''"(x) "d"x = int(6x^2 - 6x + 5) "d"x`
f(x) = `(6x^3)/3 - (6x^2)/2 + 5x + "c"`
f(x) = 2x3 – 3x2 + 5x + c
But f(1) = 30
2(1)3 – 3(1)2 + 5(1) + c = 30
2 – 3 + 5 + c = 30
c = 26
f(x) = 2x3 – 3x2 + 5x + 26
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