Answer: 5
Step-by-step explanation:
- The average rate of change for the function f(x) from x=a to x=b is given by :-
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
The given function : [tex]f(x)=x^2+2x+3[/tex] (Its a quadratic function with degree 2.)
The average rate of change for the quadratic function from x=−2 to x = 5 will be :-
[tex]\dfrac{f(5)-f(-2)}{5-(-2)}\\\\=\dfrac{((5)^2+2(5)+3)-((-2)^2+2(-2)+3)}{5+2}[/tex] [Note (-)(-)=(+)]
[tex]=\dfrac{25+10+3-(4-4+3)}{7}\\\\=\dfrac{38-(3)}{7}\\\\=\dfrac{35}{7}=5[/tex]
Hence, the average rate of change for the quadratic function from x=−2 to x = 5 is 5 .
