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For the function
f(x)=x^(2)-4, find the slope of the secant line between
x=-4 and
x=-1.
Answer:

For the function $f(x)=x^{2}-4$ , find the slope of the secant line between $x=-4$ and $x=-1$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-4

, find the slope of the secant line between

x=-4

and

x=-1

.

\newline

Answer:

Formula for Slope: To find the slope of the secant line between two points on a function, we use the formula for slope, which is the change in $y$ divided by the change in $x$ (rise over run). The slope of the secant line between two points $(x_1, f(x_1))$ and $(x_2, f(x_2))$ is given by $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$ .
Find Y-Values: First, we need to find the y-values for the points where $x = -4$ and $x = -1$ by plugging these x-values into the function $f(x) = x^2 - 4$ . For $x = -4$ : $f(-4) = (-4)^2 - 4 = 16 - 4 = 12$ . For $x = -1$ : $f(-1) = (-1)^2 - 4 = 1 - 4 = -3$ .
Calculate Slope: Now we have two points: Point A $(-4, 12)$ and Point B $(-1, -3)$ . We can use these points to calculate the slope of the secant line. $\text{Slope} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} = \frac{(-3 - 12)}{(-1 - (-4))} = \frac{(-3 - 12)}{(-1 + 4)} = \frac{(-15)}{3} = -5.$

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