Question

Use the following graph of the function f(x) = −3x4 − x3 + 3x2 + x + 3 to answer this question: graph of negative 3 x to the fourth, minus x cubed, plus 3 x squared, plus x plus 3 What is the average rate of change from x = 0 to x = 1?

Answer 1

Answer:

The average rate of change from x=0 to x=1 for f(x) is 0.

Step-by-step explanation:

We are given the function $f(x)=-3x^{4}-x^{3}+3x^{2}+x+3$.

Now, the rate average rate of change of a function from $y=x_{1}$ to $y=x_{2}$ is given by $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$.

As, we need the rate of change from x = 0 to x = 1.

So, we will find the values of f(0) and f(1).

i.e. $f(0)=-3\times0^{4}-0^{3}+3\times0^{2}+0+3$ i.e. f(0)  = 3

and $f(1)=-3\times1^{4}-1^{3}+3\times1^{2}+1+3$ i.e. $f(1)=-3-1+3+1+3$ i.e. f(1) = 3

Thus, the rate of change from x=0 to x=1 is $\frac{f(1)-f(0)}{1-0}$ i.e.  $\frac{3-3}{1-0}$ i.e. 0

Hence, the average rate of change from x=0 to x=1 for f(x) is 0.