For the given function, find the slope of the secant line through the points where x has the given values x = -3 and x = 1.

f(x)=x2+x


To find the slope of the secant line through the points where \( x = -3 \) and \( x = 1 \) for the function \( f(x) = x^2 + x \), follow these steps:

1. **Calculate \( f(-3) \):**
   \[
   f(-3) = (-3)^2 + (-3) = 9 - 3 = 6
   \]

2. **Calculate \( f(1) \):**
   \[
   f(1) = (1)^2 + 1 = 1 + 1 = 2
   \]

3. **Find the slope of the secant line:**
   The formula for the slope of the secant line between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
   \[
   m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
   \]

   Substituting the values we found:
   \[
   m = \frac{f(1) - f(-3)}{1 - (-3)} = \frac{2 - 6}{1 + 3} = \frac{-4}{4} = -1
   \]

So, the slope of the secant line is \( m = -1 \).

Would you like more details or have any questions?

---

### Related Questions:
1. What is the equation of the secant line between these two points?
2. How do you find the derivative of the function \( f(x) = x^2 + x \)?
3. What is the slope of the tangent line to the function \( f(x) = x^2 + x \) at \( x = 1 \)?
4. How do you find the average rate of change of the function over the interval \([-3, 1]\)?
5. What is the y-intercept of the secant line between these two points?

**Tip:** The slope of a secant line represents the average rate of change of the function over a specified interval.

For the given function, find the slope of the secant line through the points where x has the given values x = -3 and x = 1. f(x) = x^2 + x

Learn how to find the slope of the secant line for the quadratic function f(x) = x^2 + x between the points x = -3 and x = 1. This problem explains the secant line slope formula and involves key algebraic concepts. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation