Question:
If $g(x)=x^{2}-x, x\in\mathbb{R},$ then $g(x)$ is increasing in ________.
If $g(x)=x^{2}-x, x\in\mathbb{R},$ then $g(x)$ is increasing in ________.
Show Hint
To find increasing intervals, solve $f'(x) > 0$.
Updated On: Jun 26, 2026
- $(-\infty,\infty)$
- $(-\infty,0)$
- $(0,-\infty)$
- (-5,5)
- $(\frac{1}{2},\infty)$
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The Correct Option is
Solution and Explanation
Step 1: Concept
A function is increasing where its derivative $g'(x) > 0$.
Step 2: Meaning
Find the derivative of $g(x) = x^2 - x$.
Step 3: Analysis
$g'(x) = 2x - 1$. Set $2x - 1 > 0 \implies 2x > 1 \implies x > \frac{1}{2}$.
Step 4: Conclusion
The function is increasing in the interval $(\frac{1}{2}, \infty)$. Final Answer: (E)
A function is increasing where its derivative $g'(x) > 0$.
Step 2: Meaning
Find the derivative of $g(x) = x^2 - x$.
Step 3: Analysis
$g'(x) = 2x - 1$. Set $2x - 1 > 0 \implies 2x > 1 \implies x > \frac{1}{2}$.
Step 4: Conclusion
The function is increasing in the interval $(\frac{1}{2}, \infty)$. Final Answer: (E)
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