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Prove that the function f given by f(x) ...

Prove that the function f given by `f(x) = | x - 1|, x in R` is not differentiable at `x = 1`

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To prove that the function \( f(x) = |x - 1| \) is not differentiable at \( x = 1 \), we need to check the left-hand derivative and the right-hand derivative at that point. ### Step-by-Step Solution: 1. **Definition of Differentiability**: A function \( f(x) \) is said to be differentiable at a point \( x = a \) if the left-hand derivative and the right-hand derivative at that point are equal. 2. **Finding the Left-Hand Derivative**: ...
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Knowledge Check

  • The function f:R to R given by f(x)=x^(2)+x is

    A
    one-one nad onto
    B
    one-one and into
    C
    many-one and onto
    D
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