COMEDK · Maths · 27. Application of Derivatives
If \(f(x) = x^3 + \dfrac{3}{2}x^2 + 3x + 3\), then \(f(x)\) is
- A Odd function
- B Even function
- C Increasing function
- D Decreasing function
Answer & Solution
Correct Answer
(C) Increasing function
Step-by-step Solution
Detailed explanation
Given function is \(f(x) = x^3 + \dfrac{3}{2}x^2 + 3x + 3\). Differentiating with respect to \(x\), we get: \(f'(x) = 3x^2 + 3x + 3\) \(f'(x) = 3(x^2 + x + 1)\) The discriminant of the quadratic \(x^2 + x + 1\) is \(D = 1^2 - 4(1)(1) = -3 0\) for all \(x \in \mathbb{R}\).…
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