Determine if the piecewise defined function is differentiable at the origin.
-$$f ( x ) = \left\{ \begin{array} { l l }
6 x - 7 & \text { if } x

Question

Determine if the piecewise defined function is differentiable at the origin.
-$$f ( x ) = \left\{ \begin{array} { l l } 
6 x - 7 & \text { if } x < 0 \
x ^ { 2 } + 5 x + 7 & \text { if } x \geq 0
\end{array} \right.$$
A) D ifferentiable
B) Not differentiable

Quizplus · Accepted Answer

For a function to be differentiable at a point, it must be both continuous at that point and have a defined derivative. In this case, the two branches of the function have different expressions at the origin, namely $6x-7$ and $7$. Therefore, the function is not continuous at the origin, and thus cannot be differentiable at the origin.

Determine If the Piecewise Defined Function Is Differentiable at the Origin