Posted by **Rochelle F** on Wednesday, April 11, 2012 at 8:45pm.

find the absolute minimum value on (0,infinity)...f(x)= x-(1/x)+(2/x^3)..

The example given is x-(1/x)+(10/x^3) which is F(sqrt5)=(6/sqrt5)

- calculus -
**Steve**, Thursday, April 12, 2012 at 12:20am
f = x - 1/x + 2/x^3

f' = 1 + 2/x^2 - 6/x^4

= (x^4 + 2x^2 - 6)/x^4

f'=0 when x^4 + 2x^2 - 6 = 0

x^2 = -1 ± √7

-1 - √7 < 0. so we have

x^2 = -1 + √7

x = ±√(√7 - 1)

we want x in (0,∞), so

f(1.28287) = 1.451

or, more exactly,

f(√(√7 - 1)) = √((97√7 - 143)/54)

## Answer this Question

## Related Questions

- Pre-Calculus - I need help-I do not understand. The question is this: Write 2x+y...
- ALGEBRA 1 - change 50 to 25*2 sqrt 50 = 5 sqrt2 change 8 to 4*2 Nope: (sqrt3-...
- calculus - PLEASE write 2x+y=5 in polar form. a. -sqrt5 = r cos (theta -...
- algebra - what is the perimeter of a square with sides that are sqrt3 + sqrt5 on...
- algebra - Can someone please check my work on this problem? For some reason, I ...
- algebra - evaluate and simplify 6 - square root20 ----------------- 2 The square...
- preCal help please - rationalized the denominator of the expression5 sqrt -3 ...
- Algebra II - I keep getting different answers, can someone help? (16^sqrt5...
- Algebra 1 - sqrt5 -1/x = sqrt5/2 i cross multiplied and i got 3.5= 2.23x is that...
- math - From the question before, I got to 18+6*SQRT5+6*SQRT5+12 am I on the ...

More Related Questions