Exercise 6 | Wiskunde op Tilburg University

Determine by the use of the property of the derivative for the function

$y(x)=3x-2\ln(x)$ how much

$x$ should approximately change to obtain the function value

$3\frac{1}{2}$ given that

$x=1$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$\Delta x \approx -\frac{1}{2}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$\Delta x \approx 1$

Antwoord 3 correct

Fout

Antwoord 4 optie

$\Delta x \approx -1$

Antwoord 4 correct

Fout

Antwoord 1 optie

$\Delta x \approx \frac{1}{2}$

Antwoord 1 feedback

Correct:

$\Delta y \approx y'(x) \cdot \Delta x$ .

$\Delta y = 3\frac{1}{2}- y(1)= 3\frac{1}{2} -(3\cdot 1 - 2\ln(1))=\frac{1}{2}$ .

$y'(x)=3-\frac{2}{x}$ . Consequently,

$y'(1)=3-\frac{2}{1}=1$ .

Hence,

$\Delta x \approx \dfrac{\Delta y}{y'(1)}=\dfrac{\frac{1}{2}}{1}=\frac{1}{2}$ .

Go on.

Antwoord 2 feedback

Wrong:

$\Delta y \neq 3\frac{1}{2} - y(1)$ .

Try again.

Antwoord 3 feedback

Wrong:

$\Delta x \not\approx y'(1)$ .

See Property derivative.

Antwoord 4 feedback

Wrong:

$\Delta x \not\approx y'(1)$ .

See Property derivative.