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The problem in the image asks to find the slope of the tangent line to the curve \( y = x^2 - 3x + 2 \) at two points: \( x = -2 \) and \( x = 1.5 \).

Here’s how we can solve this:

### Step 1: Find the derivative of the curve
To find the slope of the tangent line, we need to compute the derivative of the function \( y = x^2 - 3x + 2 \). The derivative of this function gives the slope of the tangent line at any point \( x \).

\[
\frac{dy}{dx} = \frac{d}{dx}(x^2 - 3x + 2) = 2x - 3
\]

### Step 2: Evaluate the derivative at the given points

1. For \( x = -2 \):
\[
\frac{dy}{dx}\bigg|_{x=-2} = 2(-2) - 3 = -4 - 3 = -7
\]
So, the slope at \( x = -2 \) is \( -7 \).

2. For \( x = 1.5 \):
\[
\frac{dy}{dx}\bigg|_{x=1.5} = 2(1.5) - 3 = 3 - 3 = 0
\]
So, the slope at \( x = 1.5 \) is \( 0 \).

### Final Answer:
- The slope of the tangent line at \( x = -2 \) is \( -7 \).
- The slope of the tangent line at \( x = 1.5 \) is \( 0 \).

Would you like more details or further explanation on any of the steps?

Here are some related questions for further practice:
1. How do you find the equation of a tangent line given a curve and a point?
2. What is the geometrical interpretation of a slope of zero for a tangent line?
3. How would you compute the slope of the tangent line for higher-order polynomials?
4. How can you use derivatives to determine if a function is increasing or decreasing at a specific point?
5. Can you find the second derivative of the function and explain its significance?

**Tip:** The slope of the tangent line tells you the rate of change of the function at a specific point. When the slope is zero, the tangent line is horizontal, indicating a local maximum or minimum.

Cari kemiringan garis singgung pada kurva y = x^2 - 3x + 2 di titik-titik x = -2; 1,5.

Learn how to find the slope of the tangent line to the curve y = x^2 - 3x + 2 at the points x = -2 and x = 1.5. This problem involves differentiation and understanding the behavior of quadratic functions.

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