$13$ Points$]$

LARCALCET$7$

$3\mathrm{.}6\mathrm{.}005.$MI$.$SA$.$

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Tutorial Exercise

Verify that $f$ has an inverse function. Then use the function $f$ and the given real number $a$ to find $(f^{-1}{)}^{\text{'}}(a).($Hint: See Example $1.$ If an answer does not exist, enter DNE.$)$

$f(x)=x^3-4,a=23$

Step $1$

The given function is $f(x)=x^3-4.$ Differentiate $f(x)$ with respect to $x.$

$f^{\text{'}}(x)=$

$$

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