Question

f(x)=x+1/x
Find all critical numbers.
Find where the function is increasing and decreasing.
Find critical points and identify each as a relative maximum, relative minimum, or neither.
Find second order critical numbers and tell where the graph is concave up and where it is concave down.

Answer 1

find the first derivative of the function to calculate the critical points and to find where the function is increasing and decreasing. then use the second derivative to find if the graph is concave up and where it is concave down.

Answer 2

I know this but tell me how to trace the graph.

Answer 3

The graph is a rectangular hyperbola. How to show this in written?

Answer 4

i'm not sure how to show it in written..
but what i did when i'm solving this is
first need to find the zeros of the first derivative and make a positive negative table
and from there i can be able to tell if it is inreasing or decreasing
then the second derivative i used to determine if it is concave up or concave down
after all of this i will sketch the graph..

i'm not sure if this helps.. sorry

Answer 5

The second derivative is 2/x^3. Now how to find whether it's concave up or concave down? I can't find the second order critical numbers because the term with x is in denominator.

Answer 6

whats the first derivative?

Answer 7

1-1/x^2

Answer 8

it will be concave up if f"(x)>0, concave down if f"(x)<0

Answer 9

Yes, right. But how to find second order critical numbers? I have to show the second order critical numbers also.

Answer 10

wait..(still thinking) just give me a sec. i need to find my notes

Answer 11

Okay! Take your time

Answer 12

i'm just finished calculus, and i'm messing it up again..lol

Answer 13

*I

Answer 14

hahaha...

Answer 15

The same happens with me also. Many times...

Answer 16

Yes... then?

Answer 17

.i don't know.. really sorry..

@Hero, @thomaster and @imranmeah91

Answer 18

Okay... thanks for trying. :)

Answer 19

I doubt if this is going to be helpful. But, here is a plot of:
the function
f(x)=x+1/x http://fooplot.com/plot/hs8gcysc6e
1-1/x^2 http://fooplot.com/plot/s9uz9qnqhu
2/x^3 http://fooplot.com/plot/l7u7mzkpgz

Answer 20

i have an idea,.!!!!!!! i said before that you can fin the critical points when f"(X)=undefined so: