I'm trying to understand this problem but having a hard time. Any help to point me in the right direction will be appreciated thanks
For what value(s) of the constant c is the following function continuous on (−∞,∞)?
f(x) = cx+1, x (less then or equal) 2 and cx^2, x > 2
Sorry about the format. It's supposed to be set up to look like a piecewise function but i can't seem to get it like that
For a function to be continuous the "Right hand limit" and "Left hand limit" must be approaching the same number for any give number.
Both of those functions in the piecewise are continuous from negative infiniti to positive infiniti. But since at x=2 where the piecewise function 'switches functions' the two functions are not approaching the same number from the left and the right.
So you must plug in a value for 'c' that will make them approach the same number. You do this by setting the two equations equal to each other, so at that point both parts of the piecewise equal the same number, and are therefore, (in this case at least), approaching the same number.