Final answer:
The average rate of change of the function f(x) = -2x³ + 3x² from x = -1 to x = 3 is -7.
Step-by-step explanation:
To find the average rate of change of the function f(x) = -2x³ + 3x² from x = -1 to x = 3, we use the formula for the average rate of change Avg = ∆f/∆x = (f(b) - f(a))/(b - a), where 'a' and 'b' are the given x-values.
First, calculate the function values at x = -1 and x = 3, respectively:
- f(-1) = -2(-1)³ + 3(-1)² = -2(1) + 3(1) = 1
- f(3) = -2(3)³ + 3(3)² = -2(27) + 3(9) = -54 + 27 = -27
Next, use these values to find the average rate of change:
Avg = (f(3) - f(-1))/(3 - (-1))
Avg = (-27 - 1)/(3 - (-1))
Avg = (-28)/(4) = -7
Therefore, the average rate of change of the function from x = -1 to x = 3 is -7.