Exercise 7 | Wiskunde op Tilburg University

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

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).