TS EAMCET · Maths · Continuity and Differentiability
If the function \(g(x)=\left\{\begin{array}{cl}\mathrm{K} \sqrt{x+1} &, 0 \leq x \leq 3 \\ \mathrm{~m} x+2 &, 3 < x \leq 5\end{array}\right.\) is differentiable, then \(\mathrm{K}+\mathrm{m}=\)
- A \(4\)
- B \(2\)
- C \(6\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\( \lim_{x \to 3^-} g(x) = \lim_{x \to 3^+} g(x) \Rightarrow K\sqrt{3+1} = 3m+2 \Rightarrow 2K = 3m+2 \) \( g'(x) = \left\\{\\begin{array}{ll}\\frac{K}{2\\sqrt{x+1}} &, 0…
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