SOLUTION: 1) The line y= 3x + 4 is a tangent to the curve y=ax3+bx2 +2x+7 at the point (1,7) 1a.) Determine the values of a and b 1b. ) The tangent to the curve is parallel to y= 3x +4 a

Question 1137358: 1) The line y= 3x + 4 is a tangent to the curve y=ax3+bx2 +2x+7 at the point (1,7)
1a.) Determine the values of a and b
1b. ) The tangent to the curve is parallel to y= 3x +4 at one additional point. Determine the x-coordinate of this point
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

1) The line is a tangent to the curve at the point (,)
1a.) Determine the values of and
use given point (,) and plug coordinates in
in this case, the curve must go through (,)

....solve for
.....eq.1

and the derivative of is
'=
at this point must be (the slope of the tangent):

...solve for

.......eq.2
from eq.1 and eq.2 we have
...solve for
....both sides multiply by

go to eq.1
.....eq.1 substitute

1b. ) The tangent to the curve is parallel to at one additional point. Determine the x-coordinate of this point.
For part b, you will need to solve a quadratic using the values of a and b to find the point where the derivative is again = .
'=

-> already given in point (,)
->->the x-coordinate of this point

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