Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value.
f(x) = 4x3 − 3x2, [−1, 2]
4 answers
see the related questions below. Just use your function instead.
Didn't work
boy, you don't give much away, do you?
The average value is
∫[a,b] f(x) dx
------------------
b-a
So, what didn't work?
∫[-1,2] 4x^3-3x^2 dx
= x^4-x^3 [-1,2]
= (16-8)-(1+1)
= 6
6/3 = 2
So, where is f(x)=2?
4x^3-3x^2=2
x ≈ 1.137
The average value is
∫[a,b] f(x) dx
------------------
b-a
So, what didn't work?
∫[-1,2] 4x^3-3x^2 dx
= x^4-x^3 [-1,2]
= (16-8)-(1+1)
= 6
6/3 = 2
So, where is f(x)=2?
4x^3-3x^2=2
x ≈ 1.137
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