Final answer:
The average rate of change of the function f(x)=x^4+3x^3−5x^2+2x−2 from x=-1 to x=1 is calculated using the formula ARC=f(b) - f(a) / b - a, which results in an average rate of change of 5.
Step-by-step explanation:
To calculate the average rate of change of the function f(x)=x^4+3x^3−5x^2+2x−2 from x=-1 to x=1, we use the formula for the average rate of change ARC=f(b) - f(a) / b - a, where f(x) is our function, a and b are the points we're considering. In this case, a=-1 and b=1.
First, we find the value of the function at these points:
f(-1)=(-1)^4+3(-1)^3−5(-1)^2+2(-1)−2 = 1 - 3 - 5 - 2 - 2 = -11
f(1)=(1)^4+3(1)^3−5(1)^2+2(1)−2 = 1 + 3 - 5 + 2 - 2 = -1.
Next, we apply the formula for ARC:
ARC = f(1) - f(-1) / 1 - (-1) = -1 - (-11) / 1 + 1 = 10 / 2 = 5.
Therefore, the average rate of change of the function from x=-1 to x=1 is 5.