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