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1. Hey guys, I was stuck with a question where I don't understand what to do with a question...

f'(x) = x^2 - 2 + x^-2

a) Find the value of f''(x) at x=4
For that, I got 7.97

b) Given that f(3)=0, find f(x)
I'm not sure about this part, I got f(x) = (1/3)x^3 - 2x - (1/2)x^-1 - (17/6)

c) Prove that f is an increasing function.
I don't have a clue where to start

Any help would be greatly appreciated
2. (Original post by Amit619)
Hey guys, I was stuck with a question where I don't understand what to do with a question...

f'(x) = x^2 - 2 + x^-2

a) Find the value of f''(x) at x=4
For that, I got 7.97

b) Given that f(3)=0, find f(x)
I'm not sure about this part, I got f(x) = (1/3)x^3 - 2x - (1/2)x^-1 - (17/6)

c) Prove that f is an increasing function.
I don't have a clue where to start

Any help would be greatly appreciated
For part b). You know f'(x), so f(x) is just the integral of that. However, when you integrate you get left with a constant, which we don't know. But we do know that f(3)=0, so then it just becomes a simple case of rearranging your integral. You've almost got it, but you're wrong in a few places.

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