`f:[0,2pi]rarr[-1,1]` and `g:[0,2pi]rarr[-1,1]` be respectively given by `f(x)=sin` and `g(x)=cosx`.
Define `h:[0,2pi]rarr[-1,1]` by `h(x)={("max"{f(x),g(x)} "if"0lexlepi),("min"{f(x),g(x)} "if" piltxle2pi):}` number of points at which `h(x)` is not differentiable is

Explanation

To solve the problem, we need to analyze the functions \( f(x) = \sin x \) and \( g(x) = \cos x \) over the interval \([0, 2\pi]\) and determine the points where the function \( h(x) \) is not differentiable.

### Step 1: Identify the points of intersection of \( f(x) \) and \( g(x) \)

To find the points where \( f(x) \) and \( g(x) \) intersect, we set:

\[ \sin x = \cos x \]

This can be rewritten as:

\[ \tan x = 1 \]

The solutions for \( \tan x = 1 \) in the interval \([0, 2\pi]\) are:

\[ x = \frac{\pi}{4} + n\pi \quad (n \in \mathbb{Z}) \]

Thus, within the interval \([0, 2\pi]\), the points of intersection are:

\[ x = \frac{\pi}{4} \quad \text{and} \quad x = \frac{5\pi}{4} \]

### Step 2: Define \( h(x) \)

The function \( h(x) \) is defined as follows:

- For \( 0 \leq x \leq \pi \), \( h(x) = \max(\sin x, \cos x) \)
- For \( \pi < x \leq 2\pi \), \( h(x) = \min(\sin x, \cos x) \)

### Step 3: Analyze \( h(x) \) in the intervals

1. **For \( 0 \leq x \leq \pi \)**:
- \( h(x) = \sin x \) when \( \sin x \geq \cos x \)
- \( h(x) = \cos x \) when \( \cos x \geq \sin x \)

The point of intersection \( x = \frac{\pi}{4} \) is where \( h(x) \) switches from \( \cos x \) to \( \sin x \).

2. **For \( \pi < x \leq 2\pi \)**:
- \( h(x) = \sin x \) when \( \sin x \leq \cos x \)
- \( h(x) = \cos x \) when \( \cos x \leq \sin x \)

The point of intersection \( x = \frac{5\pi}{4} \) is where \( h(x) \) switches from \( \sin x \) to \( \cos x \).

### Step 4: Identify points of non-differentiability

The function \( h(x) \) is not differentiable at points where it switches between \( \max \) and \( \min \). Therefore, we have:

- At \( x = \frac{\pi}{4} \): \( h(x) \) switches from \( \cos x \) to \( \sin x \).
- At \( x = \frac{5\pi}{4} \): \( h(x) \) switches from \( \sin x \) to \( \cos x \).
- At \( x = \pi \): \( h(x) \) changes from \( \max \) to \( \min \).

### Conclusion

Thus, the total number of points where \( h(x) \) is not differentiable is:

\[ \text{Number of points} = 3 \quad \text{(at } x = \frac{\pi}{4}, \, x = \pi, \, x = \frac{5\pi}{4}\text{)} \]

### Final Answer

The number of points at which \( h(x) \) is not differentiable is **3**.

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