Verify Lagranges mean value theorem for function `f(x)=tan^(-1)x` on `[0,\ 1]` and find a point `' c '` in the indicated interval:

Answer

At ` c=sqrt{frac{4}{pi}-1} approx 0.52 in(0,1)`

Hence, LMVT is verified.

Explanation

ATQ,

$$ f(x)=\tan ^{-1} x \text { on }[0,1]
$$
`\tan ^{-1} x` has unique value for all `x` between 0 and `1 .`

`\therefore f(x)` is continuous in `[0,1]`

$$
f(x)=\tan ^{-1} x
...