Question

question
for the function ( f(x)=x^{2}+6 ), find the slope of the secant line
between ( x=-3 ) and ( x = 3 ).

Explanation:

Step1: Find the function values at $x = - 3$ and $x = 3$

When $x=-3$, $f(-3)=(-3)^{2}+6=9 + 6=15$.
When $x = 3$, $f(3)=3^{2}+6=9+6=15$.

Step2: Use the slope formula for the secant line

The slope formula for the secant line between two points $(x_1,f(x_1))$ and $(x_2,f(x_2))$ is $m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here $x_1=-3$, $x_2 = 3$, $f(x_1)=15$, $f(x_2)=15$. Then $m=\frac{15 - 15}{3-(-3)}=\frac{0}{6}=0$.

Answer:

$0$