How do you find the numbers b such

Jakobe Norton

Jakobe Norton

Answered question

2022-04-11

How do you find the numbers b such that the average value of f(x)=7+10x9x2 on the interval [0, b] is equal to 8?

Answer & Explanation

libertydragonrbha

libertydragonrbha

Beginner2022-04-12Added 15 answers

The average value of f(x)=7+10x9x2 on the interval [0,b] is
1b00b(7+10x9x2)dx
Which can be evaluated to,
1b[7x+5x23x3]0b=7b+5b23b3b
=7+5b3b2
We want the average value to be 8, so we need to solve
7+5b3b2=8.
Use the formula or complete the square to get
two solutions: b=5136andb=5+136
Since both are positive, the interval [0,b] exists for either of these.
mislifola5vo

mislifola5vo

Beginner2022-04-13Added 11 answers

The average rate of change of f(x) on the interval [a,b] is f(b)f(a)ba
We have that a=0, b=b, f(x)=9x2+10x+7
Thus, f(b)f(a)ba=7+10b9b2(7+10(0)9(0)2)b(0)=9b2+10bb=109b
Answer: 10-9b

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