Which of the following properties are satisfied by the following function: f(x) = $\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.$ (I) f(x) is continuous
(II) f(x) is differentiable for all x
(III) f(x) is differentiable at x = -2

Question

Which of the following properties are satisfied by the following function: f(x) = $\left\{ \begin{array} { l l } 
x ^ { 2 } + 1 & \text { for } x < 0 \
1 & \text { for } x = 0 \
5 x + 1 & \text { for } x > 0
\end{array} \right.$ (I) f(x) is continuous 
(II) f(x) is differentiable for all x
(III) f(x) is differentiable at x = -2
A) III only
B) I only
C) I, II, and III
D) I and II only
E) I and III only

Quizplus · Accepted Answer

The Answer of Which of the following properties are satisfied by the following function: f(x) = $\left\{ \begin{array} { l l } 
x ^ { 2 } + 1 & \text { for } x < 0 \
1 & \text { for } x = 0 \
5 x + 1 & \text { for } x > 0
\end{array} \right.$ (I) f(x) is continuous 
(II) f(x) is differentiable for all x
(III) f(x) is differentiable at x = -2
A) III only
B) I only
C) I, II, and III
D) I and II only
E) I and III only

Which of the Following Properties Are Satisfied by the Following {x2+1 for x<01 for x=05x+1 for x>0\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.⎩⎨⎧​x2+115x+1​ for x<0 for x=0 for x>0​

Which of the Following Properties Are Satisfied by the Following $\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.$