WBJEE · Maths · Application of Derivatives
For what values of \(\mathrm{x}\), the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^4-4 \mathrm{x}^3+4 \mathrm{x}^2+40\) is monotone decreasing?
- A \(0 < x < 1\)
- B \(1 < x < 2\)
- C \(2 < x < 3\)
- D \(4 < x < 5\)
Answer & Solution
Correct Answer
(B) \(1 < x < 2\)
Step-by-step Solution
Detailed explanation
Hints: \(f^{\prime}(x)=4 x^3-12 x^2+8 x=4 x\left(x^2-3 x+2\right)\) \(=4 x(x-1)(x-2)\) \(\therefore \mathrm{x}\) is decreasing for \(\mathrm{x} \in(1,2)\)
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