+1904 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.
+129907 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
