Can someone show and explain how to do this!?

Question

The function f(x)=2x+2x^-1 has one relative minimum and one relative maximum. It is helpful to make a rough sketch of the graph to see what is happening.
This function has a relative minimum at.....
with value.......
and a relative maximum at........
with value ........

Answer 1

f(x) = 2x + 2x^-1
estimate .. or use derivatives
f'(x) = 2 - 2/x^2
0 = 2 - 2/x^2
0 = 2x^2 - 2
1 = x^2
x = +- 1
Points:
(1,4) relative max
(-1,-4) relative min

Answer 2

The graph looks like:
http://img233.imageshack.us/img233/2256/graphok1.gif

The function can be rewritten as:
f(x) = 2(x + 1/x)

If you plug in values for x, you can figure out y. Graph them to see what it looks like to confirm the relative maximum and minimum.

To determine them, take the derivative and set it to zero.

f'(x) = 2 + (-1)2^x(-2)
f'(x) = 2(1 - 1/x²)

Set this to zero:
0 = 2(1 - 1/x²)
0 = 1 - x²
x² = 1

Solve for x to get the points:
x = -1 or x = 1

Then calculate the respective y values:
y = -4 or y = 4

The function has a relative minimum at x = 1, with value 4
The function has a relative maximum at x = -1, with value -4

Answer 3

relative minimum at 1 with value 4
relative maximum at -1 with value -4
get a graphing calculator =)