please help me..... The curve whose equation is y=ax^3 + bx^2 + cx + d has a point of inflexion at (-1,4), a turning point when x=2, and it passes through the point (3,-7). Find the values of a, b, c and d.

Question

anonymous · Answer

a=3/11    b=9/11   c=-72/11     d=-23/11
$$y'=3ax ^{2}+2bx+c$$
$$y''=6ax+2b$$   inflection poit at (-1,4)  means the second derivative =0 at x=1  which gives $$0=-6a+2b$$  which means b=3a  a turning point at x=2 means the first derivative =0 at x=2 which gives$$12a+4b+c=0$$  So 24a+c=0   and c=-24a use the inf that f(3)=-7 and f(-1)=4 to solve for a and d