The line $y=2x+b$ is tangent to the graph of the function $y(x)=\ln(x)$. Determine $b$.
$b=-1-\ln(2)$
$b=\frac{1}{2}$
$b=1$
$b=1\frac{76}{99}$
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.
Antwoord 2 feedback
Wrong: Do not confuse $b$ with $x$.

See Example 2 (film).
Antwoord 3 feedback
Wrong: The tangent line is not equal to the derivative function.

See Example 2 (film).
Antwoord 4 feedback
Wrong: Why do you put the derivative equal to the function?

See Example 2 (film).