Determine c so that f(x) is continuous on the entire real line if f(x)= x^2 when x3

Question

Determine c so that f(x) is continuous on the entire real line if f(x)= x^2 when x<=3 and c/x when x>3

anonymous · Answer

This is fairly simple, do you know what the definition of continuous is?

anonymous · Answer

Basically it means that if you look at the graph, it doesn't jump, we call this a smooth curve

anonymous · Answer

so basically you need to find a value of c, for the boundary point at x = 3 where the curve will be smooth

anonymous · Answer

I'll give you an example, if x = 3, f(x) = 9 right?
If c is 1, then after 3, the curve suddenly falls to 1/3, which is not smooth,
So what is the value of c that will make it smooth?

The answer is 27, from c/x = 9, where x = 3

anonymous · Answer

im sorry my computer froze and yeh i unerstand the continuous part...lemme read the rest real quick

anonymous · Answer

ohhh i understand this. It wasn't in my book and i was just very lost. thanks so much

anonymous · Answer

no problem