Find a cubic function, in the form f(x)=ax^3+bx^2+cx+d, that has a local maximum value of 4 at -3 and a local minimum value of 0 at 2.
f (x) = ax3 + bx2 + cx + d
f′(x)=3ax2+2bx+c
f(−3)=4=−27a+9b−3c+d
f(2)=0=a+b+c+d
f′(−3)=0=27a−6b+c
f′(2)=0=12a+4b+c

Question

Find a cubic function, in the form f(x)=ax^3+bx^2+cx+d, that has a local maximum value of 4 at -3 and a local minimum value of 0 at 2. 
f (x) = ax3 + bx2 + cx + d
f′(x)=3ax2+2bx+c
f(−3)=4=>−27a+9b−3c+d
f(2)=0=>a+b+c+d
f′(−3)=0=>27a−6b+c
f′(2)=0=>12a+4b+c

anonymous · Answer

(−27a+9b−3c+d=4−a+b+c+d=0)=−28a+8b−4c=4

(27a−6b+c=0−12a+4b+c=0)=12a−10b=0


(−28a+8b−4c=4+4(12a+4b+c)=0)=(−28a+8b−4c=4+48a+16b+4c=0)

=20a+24b=4


I need to isolate a and b in order to get d, then c