The line $y=2x+b$ is tangent to the graph of the function $y(x)=\ln(x)$. Determine $b$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$b=\frac{1}{2}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$b=1$
Antwoord 3 correct
Fout
Antwoord 4 optie
$b=1\frac{76}{99}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$b=-1-\ln(2)$
Antwoord 1 feedback
Correct: $y'(x)=\frac{1}{x}=2$. Hence, $x=\frac{1}{2}$.
Consequently, $2x+b=\ln(x)$ gives $2\cdot \frac{1}{2}+b=\ln(\frac{1}{2})$. Solving gives $b=\ln(\frac{1}{2})-1=-1-\ln(2)$.
Go on.
Consequently, $2x+b=\ln(x)$ gives $2\cdot \frac{1}{2}+b=\ln(\frac{1}{2})$. Solving gives $b=\ln(\frac{1}{2})-1=-1-\ln(2)$.
Go on.
Antwoord 2 feedback
Antwoord 3 feedback
Antwoord 4 feedback