For what value of the constant C is the function f continous on (-∞,∞)?

This is a piecewise function. I do not know how to type the bracket.

f(x)=Cx^2+2x if x<2

f(x)=x^3-cx if x≥2

If anyone can help and give me a step-by-step answer, I would really appreciate it. Thanks.

gibsonj338
Apr 13, 2018

#1**+1 **

f(x) = cx^2 + 2x x < 2

f(x) = x^3 - cx x ≥ 2

Let's just substitute 2 into each function for x

c(2)^2 + 2(2) = 4c + 4

(2)^3 - c(2) = 8 - 2c

Set these results equal and solve for c

4c + 4 = 8 - 2c add 2c to both sides, subtract 4 from both sides

6c = 4 divide both sides by 6

c =2/3

See the graph here that confirms the result :

https://www.desmos.com/calculator/ahns4csjpv

CPhill
Apr 13, 2018