If $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1,x < 0}\\ {1 + \sin x,0 \le x \le \frac{\pi }{2}} \end{array}} \right.$ then derivative of $f\left( x \right)$ at $x = 0$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {1,x < 0}\\ {1 + \sin x,0 \le x \le \frac{\pi }{2}} \end{array}} \right.

then derivative of

f\left( x \right)

x = 0

View answer and explanation

Correct option: D

Does not exist

Option D (Does not exist) is correct because the left-hand derivative and right-hand derivative at

x = 0

are not equal.

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