Use a graph of the function to find the derivative of the function at the given point, if it exists.
-$f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \ - x - 4 & x 2 \end{array} \quad \right.$ at $x = 2$
A) 1
B) $- 1$
C) 0
D) Does not exist

Question

Use a graph of the function to find the derivative of the function at the given point, if it exists.
-$f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \ - x - 4 & x > 2 \end{array} \quad \right.$ at $x = 2$
A) 1
B) $- 1$
C) 0
D) Does not exist

Quizplus · Accepted Answer

The derivative does not exist at $x = 2$ because the function has a sharp corner at that point. The left-hand limit of the derivative as $x$ approaches 2 is 1 (from the equation $7 + x$), and the right-hand limit is $-1$ (from the equation $-x - 4$). Since these two limits are not equal, the derivative does not exist at $x = 2$.

Use a Graph of the Function to Find the Derivative f(x)={7+xx≤2−x−4x>2f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \\ - x - 4 & x > 2 \end{array} \quad \right.f(x)={7+x−x−4​x≤2x>2​

Use a Graph of the Function to Find the Derivative $f ( x ) = \left\{ \begin{array} { l l } 7 + x & x \leq 2 \\ - x - 4 & x > 2 \end{array} \quad \right.$