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The function f (x) = x2, for all real x, is
- a)neither decreasing nor increasing
- b)Decreasing
- c)Increasing
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The function f (x) =x2, for all real x, isa)neither decreasing nor inc...
Since f ‘(x) = 2x > 0 for x > 0,and f ‘ (x) = 2x < 0 for x < 0 ,therefore on R , f is neither increasing nor decreasing. Infact , f is strict increasing on [0 , ∞) and strict decreasing on (- ∞,0].
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The function f (x) =x2, for all real x, isa)neither decreasing nor inc...
Explanation:
Reasoning:
The function f(x) = x^2 for all real x is neither decreasing nor increasing.
Reasoning:
- A function is said to be increasing if for any two values of x, x1 and x2, if x1 < x2,="" then="" f(x1)="" />< />
- On the other hand, a function is said to be decreasing if for any two values of x, x1 and x2, if x1 < x2,="" then="" f(x1)="" /> f(x2).
- In the case of the function f(x) = x^2, we can see that it is neither increasing nor decreasing.
- For example, if we take x1 = -2 and x2 = -1, we have x1 < x2,="" but="" f(x1)="(-2)^2" =="" 4="" and="" f(x2)="(-1)^2" =="" 1.="" therefore,="" f(x1)="" /> f(x2), which means that the function is not increasing.
- Similarly, if we take x1 = -1 and x2 = 2, we have x1 < x2,="" but="" f(x1)="(-1)^2" =="" 1="" and="" f(x2)="2^2" =="" 4.="" therefore,="" f(x1)="" />< f(x2),="" which="" means="" that="" the="" function="" is="" not="" />
- Thus, we can conclude that the function f(x) = x^2 is neither increasing nor decreasing.
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The function f (x) =x2, for all real x, isa)neither decreasing nor increasingb)Decreasingc)Increasingd)none of theseCorrect answer is option 'A'. Can you explain this answer?
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