Question

The function f is given by f(x)=1+3cosx. What is the average rate of change of f over the interval [0,π]?

Answer 1

Answer:

$-\frac{6}{\pi}$

Step-by-step explanation:

To find the average rate of change, we use the formula

$\frac{f(b)-f(a)}{b-a}$

Where $a=0$ and $b=\pi$

Knowing this, we can plug in all of our know values and simplify.

$\frac{1}{\pi} ((1+3cos(\pi ))-(1+3cos(0))\\\\\frac{1}{\pi} ((1-3 ))-(1+3))\\\\\frac{1}{\pi} (-2-4)\\\\-\frac{6}{\pi}$

Answer 2

The average rate of change of f over the interval [0,π] is; -6/π.

According to the question, the function f is given by f(x)=1+3cosx.

In essence, to find the average rate of change of f over the interval, [0,π];

We have to evaluate;

• {f(π) - f(0)} / π - 0

Therefore;

• f(π) = 1 + 3cosπ

where π = 180°

• f(π) = 1 + 3cos180

• f(π) = 1 + (3×-1)

• f(π) = 1 - 3.

f(π) = -2.

Also:

• f(0) = 1 + 3cos0

• f(0) = 1 + 3

• f(0) = 4

Therefore, the average rate of change is given as;

• {f(π) - f(0)} / π - 0

• = (-2 -4)/π

Ultimately, the average rate of change of f over the interval [0,π] is;

-6/π.

Read more:

https://brainly.com/question/24179906