the curve y=ax³ +bx² -x+5 has a point of inflexion at (1,-2). find the values of a and b

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31-01-2015
Mathematics

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the curve y=ax³ +bx² -x+5 has a point of inflexion at (1,-2). find the values of a and b

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konrad509 konrad509 · Answer 1 · 2015-01-31T07:37:57-05:00

konrad509 konrad509

31-01-2015

[tex]y=ax^3+bx^2-x+5\\ y'=3ax^2+2bx-1\\ y''=6ax+2b\\\\ 0=6a\cdot1+2b\\ 6a+2b=0\\ 3a+b=0\\ b=-3a\\\\ -2=a\cdot1^3-3a\cdot1^2-1+5\\ -2=a-3a+4\\ -2a=-6\\ a=3\\\\b=-3\cdot3\\ b=-9[/tex]

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