Question:
The function f defined by \(f(x) = x^3 - 3x^2 + 5x + 7\), is :
The function f defined by \(f(x) = x^3 - 3x^2 + 5x + 7\), is :
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Check the sign of f'(x) using its discriminant.
Updated On: Nov 11, 2026
- increasing in \(\mathbf{R}\).
- decreasing in \(\mathbf{R}\).
- decreasing in \((0, \infty)\) and increasing in \((-\infty, 0)\).
- increasing in \((0, \infty)\) and decreasing in \((-\infty, 0)\).
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The Correct Option is A
Solution and Explanation
\(f'(x) = 3x^2 - 6x + 5\). Its discriminant is \(36 - 60 = -24 \lt 0\) and the leading coefficient is positive, so \(f'(x) \gt 0\) for all real x.
Hence f is strictly increasing in \(\mathbf{R}\).
Answer: (1) increasing in \(\mathbf{R}\).
Hence f is strictly increasing in \(\mathbf{R}\).
Answer: (1) increasing in \(\mathbf{R}\).
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