The function $z(x,y)$ is given by $z(x,y)=4x^2y^{\frac{1}{3}}$. Determine the slope of the line tangent to the level curve through the point $(5,1)$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$-30$
Antwoord 2 correct
Fout
Antwoord 3 optie
$\dfrac{6}{5}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$30$
Antwoord 4 correct
Fout
Antwoord 1 optie
$-\dfrac{6}{5}$
Antwoord 1 feedback
Correct: $$\begin{align*}
\dfrac{z'_x(x,y)}{z'_y(x,y)}&= \dfrac{8xy^{-\frac{1}{3}}}{\frac{4}{3}x^2y^{-\frac{2}{3}}}\\
& = \dfrac{6y}{x}
\end{align*}$$
$$\begin{align*}
\textrm{slope} &=- \dfrac{6\cdot 1}{5}\\
&=-\dfrac{6}{5}\\
\end{align*}$$
Go on.
\dfrac{z'_x(x,y)}{z'_y(x,y)}&= \dfrac{8xy^{-\frac{1}{3}}}{\frac{4}{3}x^2y^{-\frac{2}{3}}}\\
& = \dfrac{6y}{x}
\end{align*}$$
$$\begin{align*}
\textrm{slope} &=- \dfrac{6\cdot 1}{5}\\
&=-\dfrac{6}{5}\\
\end{align*}$$
Go on.
Antwoord 2 feedback
Wrong: $x=5$ and $y=1$, not the other way around.
Try again.
Try again.
Antwoord 3 feedback
Wrong: The slope is not equal to the quotient of the partial derivatives.
See Tangent line to level curve.
See Tangent line to level curve.
Antwoord 4 feedback
Wrong: The slope is not equal to the quotient of the partial derivatives.
See Tangent line to level curve.
See Tangent line to level curve.