calculus
posted by help needed
y=x^3=cx and y=ax^2+bx1 have a common tangent at (1,4). find a, b, andc

Reiny
I will assume the first equation is
y = x^3 + cx (since the + and + are just a "shift" away)
since (1,4) is a common point
4 = 1  c
c = 3 , and
4 = a(1) b  1
ab = 3 (#1)
If they have a common tangent, then their slopes must be the same.
3x^2 + c = 2ax + b , but c = 3
3x^2 + 3 = 2ax + b
again (1,4) must satisfy.
3 + 3 = 2a + b
2a  b = 6 (#2)
#2  #1 > a = 3
back in #1
3  b = 3
b = 0
a= 3, b=0, and c=3
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