Continuity - find c and d

[Jess]

Determine c and d so that f(x) is continuous

f(x) =

3x^2 + cx + d, x < 3
2, x = 3
dx^2 + 3x + c, x > 3

(this is a piecewise function)

stuck on this :/

[Bath]

We went over piece-wise functions but not continuity. :(

I asked your question in Y!A though I got this:

all this is is a system of equations problem.
for it to be cont. all three must have a value of 2 at x = 3 (just plug this in each equation) you do not have to worry about the second equation but look at the top and bottom equations.
plug in 3 as x in each equation and you will get 27+3c+d=2
9+c+9d=2
multiply the bott eq by 3 and then solve for d. then plug the value for d into either the top or bottom eqs.
you will find c. fx is cont when c is -109/13 and when d is 2/13

[Jess]

thank you! :)