Geometrical Explanation of Mean Value Theorem

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Q. The abscissa of the points of the curve $y=x^3$ in the interval [–2, 2], where the slope of the tangents can be obtained by mean value theorem for the interval [–2, 2], are
[MP PET 1993]

1. $\pm \frac{2}{\sqrt{3}}$
2. $\pm \sqrt{3}$
3. $\pm \frac{\sqrt{3}}{2}$
4. \N

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Q. In [0, 1] Lagrange's mean value theorem is NOT applicable to
[IIT Screening 2003]

1. $f\left(x\right)\{\begin{array}{cc}\frac{1}{2}-x,x<& \frac{1}{2}\\ {(\frac{1}{2}-x)}^2,x\ge \frac{1}{2}& \end{array}$
2. $f\left(x\right)\{\begin{array}{cc}\frac{sinx}{x},x\ne 0& \\ 1,x=0& \end{array}$
3. f(x) = x |x|
4. f(x) = |x|

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