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The question is asking whether the function \( f(x) = 4x^2 \) has a tangent slope (tangenthældningen) of 24 at the point \((3, 36)\).

To check this, we need to:

1. Find the derivative \( f'(x) \) of the function, which gives the slope of the tangent line at any point \( x \).
2. Evaluate the derivative at \( x = 3 \) to see if the slope is 24.

### Step 1: Differentiate the function \( f(x) = 4x^2 \)
The derivative is:
\[
f'(x) = \frac{d}{dx} (4x^2) = 8x
\]

### Step 2: Evaluate \( f'(x) \) at \( x = 3 \)
\[
f'(3) = 8 \times 3 = 24
\]

### Step 3: Check the point
The point \( (3, 36) \) is indeed on the curve \( f(x) = 4x^2 \) because:
\[
f(3) = 4 \times 3^2 = 4 \times 9 = 36
\]

Since both conditions are satisfied (the point is on the curve and the slope of the tangent at \( x = 3 \) is 24), the answer to the question is **"Ja"** (Yes).

Would you like further details or have any other questions?

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Here are 5 related questions to expand on this topic:

1. How would you find the equation of the tangent line at \( x = 3 \)?
2. What is the geometrical interpretation of the derivative at a point?
3. How do you find the second derivative, and what does it represent?
4. What happens to the tangent slope if the function was \( f(x) = 4x^3 \) instead?
5. Can a function have more than one tangent line at a single point?

**Tip:** The derivative of a function gives the rate of change or slope of the tangent line at any point.

Har funktionen f(x) = 4x^2 tangenthældningen 24 i punktet (3; 36)?

Explore how to calculate the tangent slope of the quadratic function f(x) = 4x^2 at the point (3, 36). Includes a detailed solution, finding the derivative and verifying the slope at x = 3.

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