For what value of the constant is the function continuous on (-infin., +infin.)?

Question

F(x)=
cx^2+8x if x<3
x^3-cx if x >or= 3

Answer 1

This is a piecewise function with both pieces being continuous on their own accord, so the only problem is where we jump from one function to the second.

Since this occurs at x=3, we plug 3 into both piece functions. Then set them equal so the whole function is continuous.

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

Now solve for c

9c+24=27-3c
12c=3
c=1/4

Answer 2

Both parts of the function are continuos in their domain, whatever the value of c is. What you need is continuity in x=3, so both sides of the function have to be equal there. By replacing x with 3 you have, on one side:

9c + 24

On the other:

27 - 3c

So equal both and obtain:

c = 1/4

Answer 3

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

9c + 24 = 27 - 3c

12c = 3

c = 1/4