If $f(x) = \left\{ {\begin{array}{*{20}{l}} {x - 5\quad {\rm{ }}\,\,{\rm{for}}\,\,{\rm{ }}x \le 1}\\ {4{x^2} - 9{\rm{ }}\,\,{\rm{for}}\,\,{\rm{ }}1 < x < 2,{\rm{ }}\,{\rm{then }}\,\,f'\left( {{2^ + }} \right) = }\\ {3x + 4{\rm{ }}\,\,{\rm{for}}\,\,{\rm{ }}x \ge 2} \end{array}} \right.$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

f(x) = \left\{ {\begin{array}{llllllllllllllllllll} {x - 5\quad \mathrm{ }\,\,\mathrm{for}\,\,\mathrm{ }x \le 1}\\ {4{x^2} - 9\mathrm{ }\,\,\mathrm{for}\,\,\mathrm{ }1 < x < 2,\mathrm{ }\,\mathrm{then }\,\,f'\left( {{2^ + }} \right) = }\\ {3x + 4\mathrm{ }\,\,\mathrm{for}\,\,\mathrm{ }x \ge 2} \end{array}} \right.

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Correct option: C

The correct answer is C (3) because it is the limit of the derivative of the function as x approaches 2 from the right.