Maths · Limits, continuity and differentiability
\) Lagranges Mean Value theorem is NOT applicable to
\( \mathbf{n}[\mathbf{0}, \mathbf{1}] \) Lagranges Mean Value theorem is NOT applicable to
- A. \( f(x)=x|x| \)
- B. \( f(x)=|x| \)
- C. \( f(x)=x \)
- D. none of these
Step-by-step solution
Lagrange's Mean Value Theorem requires the function to be continuous on [0,1] and differentiable on (0,1). Both f(x)=x|x| and f(x)=|x| reduce to f(x)=x on [0,1], which is continuous and differentiable. f(x)=x is also continuous and differentiable. Hence the theorem applies to all three functions, so none is not applicable.
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