1a function is increasing or decreasing in a interval
asking about it "at (0,0)" or any point is meaning less
btw that function is strictly increasing in (-∞,∞)
Is the function F(x) = x^3+C ; where C belongs to positive real numbers including 0 ; always strictly increasing at (0,0) ??
please explain !!
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7 Answers
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1ok .. but what can be said about the nature of the function about the origin ??
4If it is strictly increasing in (-∞,∞) then it is also increasing at the origin
1Double differentiate the function and find f'(x). Equate f'(x) to 0, and we get x=0.
Hence at (0,0) the slope is 0.
In the intervals (-∞,0) and (0,∞) we find that the function is increasing. But at (0,0) it is neither increasing nor deceasing.
The concept of functions tells us that "For a function to be strictly increasing, every real number C belonging to the interval (A,B) , f'(C) should be greater than 0."
But we find that at x=0, f'(x) = 0.
So this function is not strictly increasing.
And besides, the concepts also tell us that "If the sign of f'(x) does not change as it passes through C, then C is a point of inflection ."
Hence, origin is a point of inflection.
This function is increasing only.
1agree with philip.
the function has a value C at (0,0).
the question of increasing or decreasing arises only in an interval.
1Yep... agree... the question of increasing or decreasing arises only in an interval.