Find the value of a, b, and c such that f(x) = ax3 + bx2 +cx see details?

Find the value of a, b, and c such that f(x) = ax3 + bx2 +cx has a minimum point at (1,-7) and a maximum point at (-2,20).

Find the value of a, b, and c such that f(x) = ax3 + bx2 +cx see details?
f ' (x)= 3ax^2+2bx+c


if (1,-7) is minimum point then


f ' (1)=0


and


f(1)=-7


f'(1)=3a+2b+c=0


a+b+c=-7


idem for (-2,20)


f'(-2)=12a+4b-c=0


f(-2)=-8a+4b-2c=20


you have a system of equation solve it and compute a,b,c.