What is the continuity test? I need to know how to solve this: given g(x) = {2x^3 -1 , x or equal to 1/3 find b such that g(x) is a continuous function. this is bc calc.

Question

What is the continuity test? I need to know how to solve this:

given g(x) = {2x^3 -1  ,   x < 1/3
                   {bx^2 +1  , x> or equal to 1/3

find b such that g(x) is a continuous function.
this is bc calc.

zzr0ck3r · Answer

when we plug in 1/3 to the top we get
2/27-1 = -25/27
we want the same thing to happen on the second part
b(1/3)^2+1 = -25/27
solve for b

anonymous · Answer

but why the same thing on the second part?

zzr0ck3r · Answer

well, we want it to be continuous and 2x^3-1 is continuous and so is the bottom one for any number b but we dont want there to be a jump when we go from the first function defined for x<1/3 to the second function. so we make sure they have the same value at the point we have a break at.

zzr0ck3r · Answer

go to wolfram and graph them both and use different values for b, I think you will understand it better

zzr0ck3r · Answer

this is just an example 
but say the graph looked like these
|dw:1379385946693:dw|
the one on the left is the top and the one on the right is the bottom for some value b
now if we find the right b we will have

zzr0ck3r · Answer

|dw:1379386018332:dw|