KCET · Maths · Application of Derivatives
The function \(f(x)=x^{2}-2 x\) is strictly decreasing in the interval
- A \((-\infty, 1)\)
- B \((1, \infty)\)
- C \(R\)
- D \((-\infty, \infty)\)
Answer & Solution
Correct Answer
(A) \((-\infty, 1)\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^{2}-2 x\) \(\therefore f^{\prime}(x)=2 x-2\) \(f(x)\) is strictly decreasing, when \(f^{\prime}(x) < 0\) \(\quad f^{\prime}(x) < 0\) \(\Rightarrow \quad 2(x-1) < 0\) \(\Rightarrow \quad x < 1\) Hence, \(f(x)\) is strictly decreasing in the interval \((-\infty, 1) .\) \((-\infty, 1)\).
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