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Consider the function f(x)=|x-2|+|x-5|,x...

Consider the function `f(x)=|x-2|+|x-5|,x in R` . Statement 1: `f'(4)=0` Statement 2: `f` is continuous in `[2, 5]`, differentiable in `(2, 5) and f(2) = f(5)`. (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

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To solve the problem, we need to analyze the function \( f(x) = |x - 2| + |x - 5| \) and evaluate the two statements provided. ### Step 1: Analyze the function The function \( f(x) \) is defined using absolute values, which means we need to consider different cases based on the values of \( x \). 1. **Case 1: \( x < 2 \)** \[ f(x) = -(x - 2) - (x - 5) = -x + 2 - x + 5 = -2x + 7 ...
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