The average rate of change between the max and min of the function is -0.35
How to determine the average rate of change
From the question, we have the following parameters that can be used in our computation:
f(x) = x⁴- x²
Differentiate the function
So, we have
f'(x) = 4x³ - 2x
Set to 0 and evaluate
4x³ - 2x = 0
This gives
2x³ - x = 0
Factor out x
x(2x² - 1) = 0
This gives
x = 0 and 2x² - 1 = 0
So, we have
x = 0 and 2x² = 1
When solved for x, we have
x = 0 and x = 1/√2
Recall that
f(x) = x⁴- x²
So, we have
f(0) = 0⁴- 0² = 0
f(1/√2) = (1/√2)⁴- (1/√2)² = -0.25
The average rate of change between the max and min of the function is
Rate = (-0.25 - 0)/((1/√2) - 0)
Evaluate
Rate = -0.35
Hence, the average rate of change is -0.35