A few days ago
um,,,,help,,,,,,,,?
Make the cubic y=ax^3+bx^2+cx+d pass through the points (0,6)(1,-2) and be tnagent to 3x-y=6 at (2,0)
Top 1 Answers
A few days ago
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Substituting the coordinates of the points (0,6), (1,-2), and (2,0) into the cubic’s equation, we get:
d = 6
a + b + c + d = -2
8a + 4b + 2c + d = 0
The line
3x-y=6
<=> y = 3x – 6
has the slope of 3.
The slope of the cubic
y’ = 3ax² + 2bx + c
must be equal to 3 at x=2:
8a + 4b + c = 3.
Solving the system of equations:
d = 6
a + b + c + d = -2
8a + 4b + 2c + d = 0
8a + 4b + c = 3
we find that
a=2
b=-1
c=-9
d=6
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