Question

Given that the average rate of change for y = f(x) over the interval [0,3] is −1, the average rate of change over the interval [2,3] is 5, and the average rate of change over the interval [2,6] is 3, determine the average rate of change over the interval [0,6].

Answer 1

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

$\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx$

Using this we can say that

$\int\limits^0_3 {f(x)} \, dx =-1(3)=-3\\\int\limits^2_3 {f(x)} \, dx =5(1)=5\\\\\int\limits^2_6 {f(x)} \, dx =4(5)=20$

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 = $\frac{12}{6} =2$

Answer is 2