Answer:
Answer is 2
Step-by-step explanation:
We know that average rate of change of a function f(x) in the interval (a,b) is
[tex]\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]
Using this we can say that
[tex]\int\limits^0_3 {f(x)} \, dx =-1(3)=-3\\\int\limits^2_3 {f(x)} \, dx =5(1)=5\\\\\int\limits^2_6 {f(x)} \, dx =4(5)=20\\[/tex]
Using properties of integration we have
3 to 6 integral = 20-5 =15
0 to2 integral = -3=5 =-8
Thus integral form 0 to 6 would be = -8+15+5 = 12
Average rate of change form 0 to 6 = [tex]\frac{12}{6} =2[/tex]
Answer is 2
