Question

for the function ( f(x)=x^{2}+3 ), find the slope of the secant line between ( x=-3 ) and ( x = 4 ).

Explanation:

Step1: Find \( f(-3) \) and \( f(4) \)

Given \( f(x)=x^{2}+3 \).
For \( x = - 3 \), \( f(-3)=(-3)^{2}+3=9 + 3=12 \).
For \( x = 4 \), \( f(4)=4^{2}+3=16 + 3=19 \).

Step2: Use the slope formula for the secant line

The slope formula for 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 \(x_1=-3,y_1 = f(-3)=12,x_2 = 4,y_2=f(4)=19\).
So \(m=\frac{19 - 12}{4-(-3)}=\frac{7}{4 + 3}\).

Step3: Simplify the expression

\(m=\frac{7}{7}=1\).

Answer:

\(1\)