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
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-> 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
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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):
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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
