Question

question
for the function ( f(x)=x^{2}+5 ), find the slope of the secant line between ( x=-4 ) and ( x=-1 ).

Explanation:

Step1: Find \( f(-4) \) and \( f(-1) \)

For \( x=-4 \), \( f(-4)=(-4)^{2}+5=16 + 5=21 \)
For \( x=-1 \), \( f(-1)=(-1)^{2}+5=1 + 5=6 \)

Step2: Use the slope formula for the secant line \( m=\frac{f(x_2)-f(x_1)}{x_2 - x_1} \)

Here \( x_1=-4,f(x_1)=21,x_2=-1,f(x_2)=6 \)
\( m=\frac{6 - 21}{-1-(-4)}=\frac{-15}{-1 + 4}=\frac{-15}{3}=-5 \)

Answer:

\(-5\)