Answer:
c = 2
Step-by-step explanation:
The function will be continuous if the limit from either side of c is the same as the value of the function at c. This will be the case if c is chosen as the x-coordinate of the point of intersection of the two expressions. In symbols, we want c = x such that ...
x^2 -6 = 4x -10
x^2 -4x +4 = 0 . . . . . add the opposite of the right side
(x -2)^2 = 0 . . . . . . . .rewrite as a square
x = 2 . . . . . . . . . . . . . take the square root and add 2
The line and parabola intersect in exactly one point (2, -2), the point of tangency of the line and the parabola. Hence choosing c=2 ensures not only continuity of the function, but also continuity of its derivative.
