Question

question
for the function $f(x)=x^{2}+2x + 4$, find the slope of the secant line between $x=-4$ and $x = 1$.

Explanation:

Step1: Find function values at given points

First, find $f(-4)$ and $f(1)$.
For $x=-4$, $f(-4)=(-4)^2 + 2\times(-4)+4=16 - 8 + 4=12$.
For $x = 1$, $f(1)=1^2+2\times1 + 4=1 + 2+4=7$.

Step2: Use slope - formula for secant line

The slope $m$ of the secant line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-4,y_1 = f(-4)=12,x_2 = 1,y_2=f(1)=7$.
So $m=\frac{f(1)-f(-4)}{1-(-4)}=\frac{7 - 12}{1+4}=\frac{-5}{5}=-1$.

Answer:

$-1$