We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Calculus help

0
262
1

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.

Apr 13, 2018

### 1+0 Answers

#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   Apr 13, 2018