You need three conditions to uniquely determine a, b and c. We have:
y(x) = ax˛+bx+c, tangent line y = 3x-5 at (2,1) and point (3,-1).
So, the conditions are:
1) y(2) = 1
2) y'(2) = 3
3) y(3) = -1
Do you understand why? If so: solve the system.
Determine so that the curve shall be tangent
to the line at (2,1) and shall also pass through (3,-1).
Since (2,1) is on the curve: .
Since (3,-1) is on the curve: .
The line has slope 3.
The slope of the tangent to the curve: .
Solve the system of equations for