#### Answer

20

#### Work Step by Step

y = $2x^{3} - 4x^{2} + 6x$ between x = -1 and x = 4
To find the rate of change, you have to use the rate of change formula:
f(b)âˆ’f(a)bâˆ’a
In this problem, the starting point is -1 and the end point is 4. Therefore, a = -1 and b = 4.
Since you know the a and b values, you can plug them into the formula:
$\frac{(2(4)^3-4(4)^2+6(4))-(2(-1)^3-4(-1)^2+6(-1))}{4-(-1)}$
= $\frac{88-(-12)}{5}$
= $\frac{100}{5}$
= 20
Therefore, the average rate of change is equal to 20.