+0  
 
0
36
1
avatar+1817 

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
Sort: 

1+0 Answers

 #1
avatar+85757 
+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

12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details