Answer:
Average rat of change of function is 6 from x = 0 to x = 1.
Step-by-step explanation:
We are given a function:
[tex]f(x) = 3x^4 - x^3 + 3x^2 + x - 3[/tex]
The attached image shows the graph for the given function.
Average rate of change of function =
[tex]\text{Average rate of change} = \displaystyle\frac{\delta y}{\delta x} = \frac{f(b)-f(a)}{b-a}[/tex]
Now we will evaluate f(1) and f(0).
[tex]f(x) = 3x^4 - x^3 + 3x^2 + x - 3\\f(1) = 3(1)^4 - (1)^3 + 3(1)^2 + (1) - 3 = 3\\f(0) = 3(0)^4 - (0)^3 + 3(0)^2 + (0) - 3 = -3[/tex]
Putting the values, we get,
[tex]\text{Average rate of change} = \displaystyle\frac{f(1)-f(0)}{1-0}\\\\= \frac{3-(-3)}{1-0} = \frac{6}{1} = 6[/tex]
Thus, the average rat of change of function is 6 from x = 0 to x = 1.
