Question

Finding average value
Calculus

Answer 1

Find the average value of g'(x) on [-π, 0] given that \[g(x) = 3^{cosx}\].

Answer 2

average value of g' on [a,b] would be
\[\frac{1}{b-a} \int\limits_a^b g'(x) dx\]

Answer 3

you do not have to find g'

Answer 4

do you know how to integrate g'(x) w.r.t. x ?

or in other words:
what function can you take the derivative of that will give you g'(x)?

Answer 5

Do i just use g(x) then?

Answer 6

g(x)

Answer 7

right the derivative w.r.t. x of g(x)+constant is g'(x)
so the integral of g'(x) w.r.t. x is g(x)+constant

we don't need the constant here since we have a definite integral

Answer 8

\[\frac{1}{b-a} \int\limits_a^b g'(x) dx=\frac{1}{b-a} g(x)|_a^b =\frac{g(b)-g(a)}{b-a}\]
so basically they could have said
what is the average rate of change from x=a to x=b of g

Answer 9

i will be back later if you have any questions

Answer 10

okay thanks

Answer 11

@freckles The answer i got was 1/pi but that is wrong what i did was \[\frac{ g(0)- g(-\pi) }{ 0-(-\pi) } \]

Answer 12

can you show me what you got for g(0) and g(-pi)