APFIVE Continuity and Differentiability of a Piecewise Function
Let $$k$$ be the function defined by $$k(x) = \begin{cases} x^2 - 1 & \text{if } x \leq 3 \\ 2x + 1 & \text{if } x > 3 \end{cases}$$. Which of the following statements about $$k$$ at $$x=3$$ is true?
A
$$k$$ is defined but neither continuous nor differentiable at $$x = 3$$.
B
$$k$$ is differentiable but not continuous at $$x = 3$$.
C
$$k$$ is continuous but not differentiable at $$x = 3$$.
D
$$k$$ is continuous and differentiable at $$x = 3$$.
Question Leaderboard
| Rank | |||||
|---|---|---|---|---|---|
| #1 | taylor11222211 | 2 | 2 | 0m 41s | 159 |
| #2 | seojinj0826 | 2 | 4 | 1m 01s | 119 |
| #3 | abrylkwong | 1 | 1 | 0m 00s | 100 |
| #4 | alexyu2008 | 1 | 1 | 0m 00s | 100 |
| #5 | lollipopleda1 | 1 | 1 | 0m 08s | 92 |
| #6 | thetitaniumgamer360 | 1 | 2 | 0m 00s | 90 |
| #7 | grace.liuu139 | 1 | 2 | 0m 07s | 83 |
| #8 | kamalkaren31 | 1 | 1 | 0m 22s | 78 |
| #9 | yieun.silver | 1 | 1 | 0m 34s | 66 |
| #10 | ibra.ahmad.awan | 1 | 1 | 0m 35s | 65 |
Items per page:
10
1 – 10 of 22