Question

Suppose f(x)=Ax^3 for x≺1 and f(x)=5-Ax for x≥1 . Find a value of A such that the function f(x) is continuous at the point x=1 .

I am little confused dealing with Ax. I am familiar on solving but again confused on how to proceed with the Ax.

Answer 1

this is much easier than it looks
replace \(x\) by \(1\) in both expressions, set them equal, solve for A

Answer 2

you got this?

Answer 3

you can do it in your head
if you put \(x=1\) you get
\[A=5-A\]

Answer 4

So would the answer be 5? Cause I got the same answer before I came onto here and it was wrong.

Answer 5

try solving
\[A=5-A\] again

Answer 6

Ah math mistake...thank you!