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UPSC NDA 2 2016 Mathematics Solved Paper

Question Numbers: 88-90

Let

\mathrm{f}(x) = \begin{cases} -2, & -3 \le x \le 0 \\ x - 2, & 0 < x \le 3 \end{cases}

and g(x) = f( | x | ) + | f(x) |

Question : 89 of 120

Marks: +1, -0

x = -2

Solution:

Concept:

Differentiate the piecewise function at the given point by using the appropriate branch.

Explanation:

The piecewise function is defined as:

g(x) = \begin{cases} -x, & -3 \le x \le 0 \\ 0, & 0 < x \le 2 \\ 2x - 4, & 2 < x \le 3 \end{cases}

x = -2

, the applicable branch is

g(x) = -x

Differentiate

g(x) = -x

with respect to

x

g'(x) = -1

Thus, at

x = -2

, the derivative (differential coefficient) is

-1

Answer:

The differential coefficient of

g(x)

x = -2

-1

Option A is correct.

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