Determine the value of the constant c for which the function is continuous at 2

Question

F(x)=(3x^2+c) if x<2

F(x)=x^3+cx if x>2 and equal to 2

Answer 1

left and right limits must agree:

as x-->2- limit is 12 + c

as x-->2+ limit is 8 + 2c

12 + c = 8 + 2c

12 = 8 + c

c=4