Solve `tan^(-1)xgtcot^(-1)x` graphically. Also find where f(x) = max. `[tan^(-1)x,cot^(-1)x]` is non-differentiable. Also find the range of `y=f(x)`.

Explanation

To solve the inequality \( \tan^{-1} x > \cot^{-1} x \) graphically and find the points of non-differentiability and the range of the function \( f(x) = \max(\tan^{-1} x, \cot^{-1} x) \), we can follow these steps:

### Step 1: Understand the Functions
The functions involved are:
- \( y = \tan^{-1} x \)
- \( y = \cot^{-1} x \)

### Step 2: Graph the Functions
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