JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \((2,3)\) be the largest open interval in which the function \(f(x)=2 \log _{\mathrm{e}}(x-2)-x^2+a x+1\) is strictly increasing and (b, c) be the largest open interval, in which the function \(\mathrm{g}(x)=(x-1)^3(x+2-\mathrm{a})^2\) is strictly decreasing. Then \(100(a+b-c)\) is equal to :
- A 420
- B 360
- C 160
- D 280
Answer & Solution
Correct Answer
(B) 360
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{f}^{\prime}(\mathrm{x})=\frac{2}{\mathrm{x}-2}-2 \mathrm{x}+\mathrm{a} \geq 0 \\ & \mathrm{f}^{\prime \prime}(\mathrm{x})=\frac{-2}{(\mathrm{x}-2)^2}-2 < 0 \\ & \mathrm{f}^{\prime}(\mathrm{x}) \downarrow \\ & \mathrm{f}^{\prime}(3) \geq 0 \\ &…
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