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  3. Chapter 2: Differentiation of functions of one variable
  4. Derivative
  5. Property derivative
  6. Exercise 2

Exercise 2

Consider the function $y(x)=^3\!\log x$. Approximate by the property of the derivative the change of the function value if $x$ decreases from $10$ to $9$.
$\dfrac{-1}{10\ln (3)}$
$^3\!\log \frac{10}{9}$
$\dfrac{1}{10}$
$\dfrac{1}{10\ln (3)}$
Consider the function $y(x)=^3\!\log x$. Approximate by the property of the derivative the change of the function value if $x$ decreases from $10$ to $9$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$^3\!\log \frac{10}{9}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$\dfrac{1}{10}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$\dfrac{1}{10\ln (3)}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$\dfrac{-1}{10\ln (3)}$
Antwoord 1 feedback
Correct: $\Delta y \approx y'(x)\Delta x=\dfrac{1}{x\ln (3)}\cdot (-1)=\dfrac{-1}{10\ln (3)}$.

Go on.
Antwoord 2 feedback
Wrong: You are asked for an approximation. Use the derivative.

See Property derivative.
Antwoord 3 feedback
Wrong: $y'(x)\neq \frac{1}{10}$.

See Derivatives elementary functions.
Antwoord 4 feedback
Wrong: The value of $x$ decreases.

Try again.