1. Home
  2. For business economics
  3. Chapter 2: Differentiation of functions of one variable
  4. Derivative
  5. Difference quotient
  6. Exercise 1

Exercise 1

Consider the function $y(x) = 2^x$. Determine the average change of the function value if $x$ increases from $x=5$ to $x=11$?
$336$.
$-336$.
$5\tfrac{1}{3}$.
$183\tfrac{3}{11}$.
Consider the function $y(x) = 2^x$. Determine the average change of the function value if $x$ increases from $x=5$ to $x=11$?
Antwoord 1 correct
Correct
Antwoord 2 optie
$-336$.
Antwoord 2 correct
Fout
Antwoord 3 optie
$5\tfrac{1}{3}$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$183\tfrac{3}{11}$.
Antwoord 4 correct
Fout
Antwoord 1 optie
$336$.
Antwoord 1 feedback
Correct: The difference quotient is $\dfrac{\Delta y}{\Delta x} = \dfrac{y(11)-y(5)}{6} = \dfrac{2048-32}{6} = 336$.

Go on.
Antwoord 2 feedback
Wrong: Pay attention to the order of $y(x)$ and $y(x+\Delta x)$ in de nominator or check how you determined $\Delta x$.

See also Example 1.
Antwoord 3 feedback
Wrong: $x+\Delta x \neq 6$, but $x+\Delta x = 5+6 = 11$.

See also Example 1.
Antwoord 4 feedback
Wrong: The increase of $x$ is $\Delta x = 11-5 = 6 \neq 11$.

See also Example 1.