COMEDK · Maths · 27. Application of Derivatives
What is the nature of the function \(f(x)=x^3-3 x^2+4 x\) on real numbers?
- A Increasing
- B Strictly decreasing
- C Decreasing
- D Constant
Answer & Solution
Correct Answer
(A) Increasing
Step-by-step Solution
Detailed explanation
The function is given by \(f(x) = x^3 - 3x^2 + 4x\). To determine the nature of the function, compute the first derivative with respect to \(x\): \(f'(x) = \dfrac{d}{dx}(x^3 - 3x^2 + 4x) = 3x^2 - 6x + 4\). Analyze the quadratic expression \(3x^2 - 6x + 4\). The discriminant…
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