473006…: “Beneath the dark hummingbird”

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Worked Out Examples Problem Videos

The following video may be helpful when trying to solve this example. Note that you may skip to the end of the video to get completion credit for this page if you don’t need to watch it.

Practice Problems: Differentiability and Continuity

1 : Is the following function differentiable at $x = \sage {p1target}$ ?

$f(x) = \begin {cases} \sage {p1f1} & x < \sage {p1target} \\ \sage {p1f2} & \sage {p1target} \leq x \end {cases}$ If $f(x)$ is differentiable at $x=\sage {p1target}$ enter $1$ in the box, if it isn’t, enter $0$ . $\answer {\sage {p1ans}}$ .

Being differentiable at $\sage {p1target}$ isn’t just about the function being continuous at that point, but it also needs the difference quotient to the right and left of that point to be the same value, so you need to check the derivative of both functions at that point to see if they agree as well!