dejamjones7171 dejamjones7171
  • 11-07-2018
  • Mathematics
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Find f. f ''(x) = −2 + 30x − 12x2, f(0) = 9, f '(0) = 14

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konrad509
konrad509 konrad509
  • 11-07-2018
[tex]\displaystyle f(x)=\iint f''(x)\, dx\, dx\\\\ f'(x)=\int (-2+30x-12x^2)\, dx\\ f'(x)=-2x+15x^2-4x^3+C\\\\ 14=-2\cdot0+15\cdot0^2-4\cdot0^3+C\\ C=14\\\\ f'(x)=-2x+15x^2-4x^3+14\\\\ f(x)=\int (-2x+15x^2-4x^3+14)\, dx\\ f(x)=-x^2+5x^3-x^4+14x+C\\\\ 9=-0^2+5\cdot0^3-0^4+14\cdot4+C\\ C=9\\\\ \boxed{f(x)=-x^2+5x^3-x^4+14x+9}[/tex]
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