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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

Text Solution

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`f(x) = |x-2| + |x-5| = 2x-5 ; x>= 5`
`= 3 ; 2<= x < 5`
`= -2x + 7 ; 2>= x`
`f\'(4) = 0`
`f(2) = 3`
`f(5) = 3`
acc to rolles theorem function is continous for (a,b)
`f(a) = f(b)`
...
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