Question

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

Answer 1

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