Question

does the equation cube root x= 1-x have a solution? use intermediate value theorem

Answer 1

HI!

Answer 2

to use the intermediate value theorem, make your function \[f(x)=x-\sqrt[3]{1-x}\]

Answer 3

if it is negative for some value of \(x\) and positive for some other value of \(x\) since it must be zero in between by the IVT

Answer 4

I dont understand.

Answer 5

I graphed the equation from both sides, but Im not sure the point where it intersects.

Answer 6

?

Answer 7

let me look

Answer 8

\[f(x)=x-\sqrt[3]{1-x}\]
\[f(0)=-1\\
f(9)=7\]

Answer 9

you can use other numbers if you like
since it is negative somewhere and positive somewhere else, it must be zero in between

Answer 10

actually you could even use \(f(2)=3\)

Answer 11

thank you so much!

Answer 12

could i ask you another question?

Answer 13

sure