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UPSC NDA I 2016 Mathematics Solved Paper

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Question Numbers: 54-55

For the next two (2) items that follow:

A function f(x) is defined as follows:

f(x)=\begin{cases} x+\pi & \text{for } x\in[-\pi,0) \\ \pi\cos x & \text{for } x\in[0,\frac{\pi}{2}] \\ \left(x-\frac{\pi}{2}\right)^{2} & \text{for } x\in(\frac{\pi}{2},\pi] \end{cases}

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Question : 55 of 120

Marks: +1, -0

Consider the following statements:

1. The function f(x) is differentiable at

x = 0

2. The function f(x) is differentiable at

x=\frac{\pi }{2}

Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

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