Question

find all critical numbers of f(x)=x+(1/x)

Answer 1

take the derivative, set it equal to zero and solve

Answer 2

can you walk me through finding the derivative

Answer 3

piece by piece
what is the derivative of \(x\) ?

Answer 4

1

Answer 5

k
and what is the derivative of \(\frac{1}{x}\) ?

Answer 6

x

Answer 7

oh no!

Answer 8

thats where im mistaken at

Answer 9

the derivative of \(\frac{1}{2}x^2\) is \(x\)

Answer 10

oh ok

Answer 11

the derivative of \(\frac{1}{x}\) is \(-\frac{1}{x^2}\)

Answer 12

so 1/x is?

Answer 13

ok so you set -1/x^2 to zero and solve

Answer 14

ok im lost in sovling this

Answer 15

ok no I use a number under 0 and a number over right

Answer 16

oh no, set
\[1-\frac{1}{x^2}=0\]

Answer 17

forgot about the 1

Answer 18

\[f(x)=1+\frac{1}{x}\]
\[f'(x)=1-\frac{1}{x^2}\] set
\[f'(x)=0\] get
\[1-\frac{1}{x^2}=0\] solve for \(x\)

Answer 19

you can solve this in your head with no algebra, or you can do algebra if you like

Answer 20

x^2=1

Answer 21

right

Answer 22

x=plus or minus 1

Answer 23

right

Answer 24

so its critical numbers would be -1,1,0

Answer 25

also \(0\) might be a critical point, but 0 is not in the domain of the original function, so it would be a miracle if it was in the domain of the derivative

Answer 26

so i would not call it a "critical point" since it is not in the domain of \(f\)
your math teacher might disagree with me

Answer 27

the hint said it had 3