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bereken het differentiequotiënt over [-2, 3]

To calculate the *differentiequotiënt* (the Dutch term for the average rate of change or difference quotient) over the interval \([-2, 3]\) for the given function \(k(x)\), we follow this process:

### Formula for the difference quotient:
\[
\frac{k(3) - k(-2)}{3 - (-2)} = \frac{k(3) - k(-2)}{5}
\]

We need to find the values of \(k(3)\) and \(k(-2)\) from the graph.

- From the graph, it appears that \(k(3) = 4\).
- Similarly, \(k(-2) = -4\).

### Now apply these values to the formula:
\[
\frac{4 - (-4)}{5} = \frac{4 + 4}{5} = \frac{8}{5} = 1.6
\]

Thus, the difference quotient over the interval \([-2, 3]\) is \(1.6\).

Would you like further details on the method used or any other explanations?

Here are 5 related questions to deepen your understanding:
1. How is the difference quotient related to the derivative of a function?
2. How can we interpret the result of the difference quotient geometrically?
3. What happens to the difference quotient as the interval becomes smaller?
4. How would the difference quotient change if the function were a straight line?
5. What is the significance of the points \(k(3)\) and \(k(-2)\) on the curve?

**Tip:** The difference quotient represents the slope of the secant line between two points on the curve. As the two points get closer, it approximates the derivative, which is the slope of the tangent line at a point.

Learn how to calculate the difference quotient over the interval [-2, 3] for the quadratic function k(x). This detailed guide explains the steps involved and covers essential calculus concepts such as the secant line and the slope of a curve. Ideal for students in Grades 10-12.

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