If the function g(x) = is differentiable, then the value of k + m is

Engineering

Mathematics

Concept of Derivative

Question

If the function g(x) = ${\begin{matrix} k \sqrt{x + 1}, & 0 \leq x \leq 3 \\ mx + 2, & 3 < x \leq 5 \end{matrix}$ is differentiable, then the value of k + m is

$\frac{10}{3}$

$\frac{16}{5}$

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By continuity of functions, we get 2k = 3m + 2 .......(A)

By differentiability of function, we get k = 4m .......(B)

$∴$ On solving (A) and (B), we get $m = \frac{2}{5}, k = \frac{8}{5}$