Exercise 1 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong:

$x=5$ and

$y=1$ , not the other way around.

Try again.

Antwoord 3 feedback

Wrong: The slope is not equal to the quotient of the partial derivatives.

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.