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For the function f(x)=|x-2|+|x-5|, where x∈ R, consider the following statements:
Statement-1: f'(4)=0
Statement-2: f is continuous on [2,5], differentiable on (2,5), and f(2)=f(5).
- Statement-1 is false, while Statement-2 is true.
- Both Statement-1 and Statement-2 are true, and Statement-2 correctly explains Statement-1.
- Both Statement-1 and Statement-2 are true, but Statement-2 does not correctly explain Statement-1.
- Statement-1 is true, while Statement-2 is false.
Correct answer: Both Statement-1 and Statement-2 are true, but Statement-2 does not correctly explain Statement-1.
Solution
Statement-1 is true because the function has a minimum at x=4, where the derivative is zero. Statement-2 is also true as the function is continuous and differentiable in the specified intervals, but it does not provide a reason for the derivative being zero at that specific point.
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