JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the function \(g\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{k\sqrt {x + 1} ,\;\;0 \le x \le 3}\\{mx + 2,\;\;3 < x \le 5}\end{array}} \right.\) is differentiable, then the value of \(k + m\) is :
- A \(4\)
- B \(2\)
- C \(\frac{{16}}{5}\)
- D \(\frac{{10}}{3}\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Since, \(g(x)\) is differentiable \( \Rightarrow g\left( x \right)\) must be continuous. \(\therefore g\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {k\sqrt {k + 1} \,\,\,,\,\,\,\,0 \le x \le 3}\\ {mx + 2\,\,\,\,\,,\,\,\,\,3 < x \le 5} \end{array}} \right.\) At…
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