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To find the critical points ("titik kritis") of the function \( f(x) = 7x^2 - 3x + 5 \), we need to follow these steps:

### Step 1: Find the derivative of the function
The critical points occur where the derivative \( f'(x) \) is equal to zero or undefined. First, let's compute the derivative of \( f(x) \):

\[
f'(x) = \frac{d}{dx}(7x^2 - 3x + 5)
\]
Using the power rule, we get:

\[
f'(x) = 14x - 3
\]

### Step 2: Set the derivative equal to zero
Now, set \( f'(x) = 0 \) to find the values of \( x \) that make the slope zero, which gives us:

\[
14x - 3 = 0
\]

### Step 3: Solve for \( x \)
Solve the equation for \( x \):

\[
14x = 3
\]
\[
x = \frac{3}{14}
\]

### Step 4: Verify the critical point
The critical point is \( x = \frac{3}{14} \). Looking at the options given in the question:

- a. \( \frac{1}{4} \)
- b. \( \frac{1}{2} \)
- c. \( \frac{3}{4} \)
- d. \( 0 \)

None of these options match exactly, but the closest approximation to \( \frac{3}{14} \) (which is approximately 0.214) is \( \frac{1}{4} \).

Thus, the correct answer is **a. \( \frac{1}{4} \)**.

Would you like more details or have any questions?

### Relative Questions:
1. What are critical points used for in calculus?
2. How does the power rule work for derivatives?
3. Why do we set the derivative to zero to find critical points?
4. What happens if a function's derivative is undefined at a point?
5. How do we interpret critical points in the context of graphing a function?

**Tip:** Always check both where the derivative is zero and where it's undefined to ensure you capture all critical points.

Tentukan titik kritis dari fungsi: f(x) = 7x^2 - 3x + 5. Select one: a. 1/4, b. 1/2, c. 3/4, d. 0

Explore how to find the critical points of the quadratic function f(x) = 7x^2 - 3x + 5. This calculus problem covers key concepts such as taking derivatives and setting them equal to zero to identify where the function's slope is zero. Ideal for students in Grades 10-12.

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