Find f.
f ''(x) = 6 − 6x − 40x^3,
f(0) = 5,
f '(0) = 6
f(x) = ?
Math Question?
2017-01-20 7:04 pm
回答 (1)
2017-01-20 7:16 pm
f“(x) = 6 - 6x - 40x^3
f’(x) = ∫f”(x)dx
f’(x) = ∫(6 - 6x - 40x^3) dx
f’(x) = 6x - 3x^2 - 10x^4 + C₁
But f’(0) = 6
6(0) - 3(0)^2 - 10(0)^4 + C₁ = 6
C₁ = 6
Then, f’(x) = 6 + 6x - 3x^2 - 10x^4
f(x) = ∫f’(x)
f(x) = ∫(6 + 6x - 3x^2 - 10x^4) dx
f(x) = 6x + 3x^2 - x^3 - 2x^5 + C₂
But f(0) = 5
6x + 3x^2 - x^3 - 2x^5 + C₂ = 5
6(0) + 3(0)^2 - (0)^3 - 2(0)^5 + C₂ = 5
C₂ = 5
Then, f(x) = 5 + 6x + 3x^2 - x^3 - 2x^5
f’(x) = ∫f”(x)dx
f’(x) = ∫(6 - 6x - 40x^3) dx
f’(x) = 6x - 3x^2 - 10x^4 + C₁
But f’(0) = 6
6(0) - 3(0)^2 - 10(0)^4 + C₁ = 6
C₁ = 6
Then, f’(x) = 6 + 6x - 3x^2 - 10x^4
f(x) = ∫f’(x)
f(x) = ∫(6 + 6x - 3x^2 - 10x^4) dx
f(x) = 6x + 3x^2 - x^3 - 2x^5 + C₂
But f(0) = 5
6x + 3x^2 - x^3 - 2x^5 + C₂ = 5
6(0) + 3(0)^2 - (0)^3 - 2(0)^5 + C₂ = 5
C₂ = 5
Then, f(x) = 5 + 6x + 3x^2 - x^3 - 2x^5
收錄日期: 2021-04-18 15:57:44
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https://hk.answers.yahoo.com/question/index?qid=20170120110416AAWSkfb