Revision questions - diff. calculus (1 Viewer)

[vanush]

15. The c urve y = ax³ + bx^2 - x +5 has a point of inflexion at (1,-2)
find the values of a and b.

?!

 

[Trev]

y=ax³+bx²-x+5, sub in (1,-2) into the equation:
-2=a+b+4
b=-a-6 (1)
y'=3ax²+2bx-1
y"=6ax+2b
Since inflection at (1,-2) then y"=0 when x=1 [6a+2b=0; b=-3a (2)]
Using (1) and (2):
-a-6=-3a ∴ a=3; b=-9.