Question

How do you find the right and left hand derivatives of a piecewise function?

Answer 1

just take them

Answer 2

\[f(x) = \left\{\begin{array}{rcc}
x^2& \text{if} & x <5 \\
2x+3& \text{if} & x\geq 5
\end{array}
\right.
\]
derivative is \[f'(x) = \left\{\begin{array}{rcc}
2x& \text{if} & x <5 \\
2& \text{if} & x>5
\end{array}
\right.
\]

Answer 3

derivative from the left at \(x=5\) is \(2\times 5=10\) while the derivative from the right is \(2\)