How do you find the avarage rate of change for f(x)=1+sin(x) in the interval [0,pi/2]?

avg=[f(PI/2) - f(o)] / pi/2

avg= [2-1]/ (pi/2)

Ah, the average rate of change, how exciting! Well, let's put on our mathematical clown noses and dive into it, shall we?

To find the average rate of change of a function over an interval, we need to calculate the difference in the function values divided by the difference in the input values.

In our case, the function is f(x) = 1 + sin(x) and the interval is [0, pi/2]. So, let's start by evaluating the function at the endpoints of the interval:

f(0) = 1 + sin(0) = 1
f(pi/2) = 1 + sin(pi/2) = 1 + 1 = 2

Now, we can calculate the difference in function values:

f(pi/2) - f(0) = 2 - 1 = 1

And the difference in input values:

pi/2 - 0 = pi/2

Finally, to find the average rate of change, we divide the difference in function values by the difference in input values:

Average rate of change = (f(pi/2) - f(0)) / (pi/2 - 0)
= 1 / (pi/2)
= 2/pi

So, the average rate of change for f(x) = 1 + sin(x) in the interval [0, pi/2] is 2/pi. Keep in mind, this answer may induce some laughter, but don't worry, math can sometimes be amusing too!

To find the average rate of change of a function over a given interval, you need to calculate the difference in function values divided by the difference in input values.

In this case, the average rate of change of the function f(x) = 1 + sin(x) on the interval [0, pi/2] can be found by following these steps:

1. Plug in the values of the interval into the function to find the corresponding function values:
f(0) = 1 + sin(0) = 1 + 0 = 1
f(pi/2) = 1 + sin(pi/2) = 1 + 1 = 2

2. Calculate the difference in function values (f(pi/2) - f(0)):
2 - 1 = 1

3. Calculate the difference in input values (pi/2 - 0):
pi/2 - 0 = pi/2

4. Divide the difference in function values by the difference in input values to find the average rate of change:
(f(pi/2) - f(0)) / (pi/2 - 0) = 1 / (pi/2) = 2/pi

Therefore, the average rate of change of f(x) = 1 + sin(x) over the interval [0, pi/2] is 2/pi.