Question

Calculate the average rate of change for the function f(x) = x4 3x3 − 5x2 2x − 2, from x = −1 to x = 1.

a) 1
b) −5
c) 5
d) −1

Answer 1

The average rate of change of the function f(x) = x⁴ - 3x³ - 5x² + 2x - 2 from x = -1 to x = 1 is calculated using the values of the function at these points. After substituting the values into the average rate of change formula, the result is -1.

Step-by-step explanation:

The question asks for the average rate of change of the function f(x) = x⁴ - 3x³ - 5x² + 2x - 2 from x = -1 to x = 1.

To calculate the average rate of change, we use the formula:

average rate of change = ∆f/∆x = (f(b) - f(a)) / (b - a)

Where 'a' and 'b' are the points on the x-axis between which we want to determine the rate of change, so here a = -1 and b = 1.

First, calculate the value of the function at x = -1 and x = 1.

• f(-1) = (-1)⁴ - 3(-1)³ - 5(-1)² + 2(-1) - 2 = 1 + 3 - 5 - 2 - 2 = -5
• f(1) = (1)⁴ - 3(1)³ - 5(1)² + 2(1) - 2 = 1 - 3 - 5 + 2 - 2 = -7

Next, apply the values to the formula:

average rate of change = (f(1) - f(-1)) / (1 - (-1)) = (-7 - (-5)) / (2) = (-2) / 2 = -1

Therefore, the average rate of change of the function over the interval from x = -1 to x = 1 is -1.