Question

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

Explanation:

Step1: Find \(f(2)\) and \(f(4)\)

For \(x = 2\), \(f(2)=2^{2}+2 + 3=4 + 2+3=9\)
For \(x = 4\), \(f(4)=4^{2}+4 + 3=16 + 4+3=23\)

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

Here \(a = 2\), \(b = 4\), \(f(a)=9\), \(f(b)=23\)
\(m=\frac{23 - 9}{4 - 2}=\frac{14}{2}\)

Answer:

\(7\)