SOLUTION: The function f, defined for x ∈ R, x>0, is such that: f'(x) =x^2 - 2+x^-2 Given that f(3)=0, find f(x). Also prove that f is an increasing function.

SOLUTION: The function f, defined for x ∈ R, x>0, is such that: f'(x) =x^2 - 2+x^-2 Given that f(3)=0, find f(x). Also prove that f is an increasing function.

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Question 1075016: The function f, defined for x ∈ R, x>0, is such that:
f'(x) =x^2 - 2+x^-2
Given that f(3)=0, find f(x). Also prove that f is an increasing function.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Integrating,

So when ,

.
.
.
Since the derivative is always positive in , the function is increasing.

.
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