Question

Complicated Algebra help!

Answer 1

The average of some functoin \(g\) on the interval \([a,b]\) is computed by
\[ \int_a^b g(x)\,dx.\]
What is the rate of change of the function \(f\) at point \(x\)?

Answer 2

* oops *
\[ \frac{1}{b-a}\int_a^b g(x)dx \]
is correct

Answer 3

!!!

Answer 4

What do you mean?

Answer 5

I honestly have never seen this

Answer 6

but it is extra credit v.v

Answer 7

`rate of change of f(x)` is another word for `variation of f(x)` -> they're talking about the derivative of \(f\).
Can you write down exactly what you have to compute?

Answer 8

Thats all the question says you want me to write it in here?

Answer 9

Nope, I let you find it yourself.

Answer 10

The answer is a number.

Answer 11

\[ f(x)=-x^2+3x+1 from x =2 \to x=5 \]

Answer 12

Ok just one number?

Answer 13

You have to compute the `average rate of change of f(x) from 2 to 5` :
\[ \int_2^5 f'(x)\,dx \]

Answer 14

* oops *
\[ \frac1{5-2}\int_2^5 f'(x)\,dx \]

Answer 15

You can compute the integral, either by differentiating first then integrating... or not differentiating at all. Since the antiderivative of the derivative is \(f\) itself.

Answer 16

I think i got it

Answer 17

-4 ?

Answer 18

Yes, i dont know what this is so i had to use a calculator

Answer 19

\[ \int_2^5 f'(x)\,dx = f(5) - f(2) = (-9) - 3 = -12 \]
-> without computing \(f'\).
then divide by 3.

Answer 20

Thank you