Please Math help for what value of the constant c is the function f continuous on (-infinity, infinity)?

its a piece wise funtction


f(x) = cx^2 + 4x if x%26lt; 2


x^3 - cx if x more than or equal to 2





Thank you for your help!

Please Math help for what value of the constant c is the function f continuous on (-infinity, infinity)?
AT x=2 one formula gives 4c+8 and the other give 8-2c. For the function to be continuous these two values should be equal.





4c+8=8-2c.





So c=0.
Reply:For what value of c is f(x) = cx^2 + 4x continuous? Well, isn't it continuous for all values of c? You're going to have a parabola for any non-zero value of c, and the line f(x) = 4x if c = 0. All parabolas and the line f(x) = 4x are continuous, so c can take any real value.