Let $f$ be the function defined by $$f(x) = \begin{cases} \sqrt{x+1} & \text{for } 0 \leq x \leq 3 \\ 5 - x & \text{for } 3 < x \leq 5. \end{cases}$$ (a) Is $f$ continuous at $x = 3$? Explain why or why not. (b) Find the average value of $f(x)$ on the closed interval $0 \leq x \leq 5$. (c) Suppose the function $g$ is defined by $$g(x) = \begin{cases} k\sqrt{x+1} & \text{for } 0 \leq x \leq 3 \\ mx + 2 & \text{for } 3 < x \leq 5, \end{cases}$$ where $k$ and $m$ are constants. If $g$ is differentiable at $x = 3$, what are the values of $k$ and $m$?
Let $f$ be the function defined by
$$f(x) = \begin{cases} \sqrt{x+1} & \text{for } 0 \leq x \leq 3 \\ 5 - x & \text{for } 3 < x \leq 5. \end{cases}$$
(a) Is $f$ continuous at $x = 3$? Explain why or why not.\\
(b) Find the average value of $f(x)$ on the closed interval $0 \leq x \leq 5$.\\
(c) Suppose the function $g$ is defined by
$$g(x) = \begin{cases} k\sqrt{x+1} & \text{for } 0 \leq x \leq 3 \\ mx + 2 & \text{for } 3 < x \leq 5, \end{cases}$$
where $k$ and $m$ are constants. If $g$ is differentiable at $x = 3$, what are the values of $k$ and $m$?