Answer the Confusing Question: Calculate f'(x) at x=2

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In summary, the question is asking for the value of the first derivative of f(x) = x^(2) - 3x - 1/x at x = 2 and in which interval this value lies. The function and its derivative do not exist at x = 0, so the interval in question is either (-\infty, 0) or (0, \infty). Since x = 2 lies in the interval (0, \infty), this is the correct answer.
  • #1
Iclaudius
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Hello friends,

I have this question which stumps me because i have no idea what its actually asking for :S - it reads:

calculate the value of the first derivative of f(x) = x^(2) -3x - 1/x at x = 2.
In which interval does it lie?

(a) -x <= x < 0
(b) 0 <= x < 4
(c) x => 4
(d) x < -2

I figure interval is related to the domain - but if we evaluate f ' (2) we get 3/4. Where this value of f ' (x) will be constantly changing (and thus no interval would exist)? So I ask what the heck are they asking of me?

Thanks in advance
 
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  • #2
First, I do NOT get 3/4 for f'(2)
f'(x)= 2x- 3+ 1/x^2 so f'(2)= 4- 3+ 1/4= 1+ 1/4= 5/4, not 3/4. Did you for get to multiply by the "n" in [itex](x^n)'= nx^{n-1}[/itex] which, here, is -1?

As for the question itself, it's not very well phrased but I think that the point is that the function and its derivative do not exist at x= 0 and so exist in the two intervals [itex](-\infty, 0)[/itex] and [itex](0, \infty)[/itex]. x= 2 lies in the second of those intervals.
 
  • #3
Hiya Hallsofivy thanks for your reply - lazy mistake on my part :yuck:
 

1. What is the meaning of f'(x)?

F'(x) represents the derivative of the function f(x), which is the rate of change of the function at a specific point.

2. How do you calculate f'(x)?

To calculate f'(x), you need to use the derivative formula, which is f'(x) = lim(h→0) [f(x+h)-f(x)]/h. This means that you find the difference between f(x) and f(x+h) and divide it by h as h approaches 0.

3. What does it mean to calculate f'(x) at x=2?

Calculating f'(x) at x=2 means finding the derivative of the function f(x) at the specific point x=2. This will give you the rate of change of the function at that point.

4. What does the value of f'(x) at x=2 tell us?

The value of f'(x) at x=2 tells us the slope of the tangent line to the function f(x) at the point x=2. This can also be interpreted as the instantaneous rate of change of the function at that point.

5. Why is it important to calculate f'(x)?

Calculating f'(x) is important because it helps us understand the behavior of a function at a specific point. It also allows us to find the maximum and minimum points of a function, as well as the intervals where the function is increasing or decreasing.

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