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.
$\Delta y = 3\frac{1}{2}- y(1)= 3\frac{1}{2} -(3\cdot 1 - 2\ln(1))=\frac{1}{2}$.
$y'(x)=3-\frac{2}{x}$. 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.
Try again.
Antwoord 3 feedback
Antwoord 4 feedback