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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
avatar+86919 
+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

 

 

cool cool cool

CPhill  Apr 13, 2018

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