This:
A cubic has a y intercept of 5 and two turning points
1,12) and (-2,15). Find the cubic
P(x)=ax^3+bx^2+cx+d P(0) = 5 = d
P'(x)=3ax^2+2bx+c
0 = 3ax^2 + 2bx + c for stat points.
0 = 3a + 2b + c 0 = 12a - 4b + c
12a - 3a - 4b -2 b + c - c = 0
9a - 6b = 0
3a - 2b = 0
P(1) = 12 P(-2) = 15
Hence, a + b + c + d = 12 -8a + 4b - 2c + d = 15
a + 8a + b - 4b + c + 2c + d - d = 12 - 15
9a - 3b + 3c = -3
3a - b + c = -1
3a - 3a + b + 2b + c - c = 0 + 1
3b = 1
b = 1/3
9a - 5(1/3) = 0
9a = 2.5
a = 5/27
3(5/27) - 1/3 + c = -1
c = -1 - 15/27 + 1/3
c = -11/9
a + b + c + d = 12
5/27 + 1/3 - 11/9 + d = 12
d = 12 - 5/27 -1/3 + 11/9
This is wrong... lol
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