Help with average value of a function

In summary, the average value of the function f(x) = 1+10x-3x^2 on the interval [0,b] can be found by integrating the function and dividing by the interval length. To solve for b, the equation f(x) = 1+10x-3x^2 must be formulated in terms of b and solved for b.
  • #1
credd741
5
0
i have a question :cry:
how would you find a number b such that the average value of
f(x)= 1+10x-3x^2 on the interval [0,b] is equal to 4.

i have tried to set this equal to 4 but everytime i try to solve for b i get some number but it is always wrong. please help!:cry::cry::cry::cry:
 
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  • #2
Welcome to the PF. How do you calculate the average of a function over an interval? What is the relevant equation?
 
  • #3
the relevant equation is the f(x)=1+10x-3x^2
 
  • #4
In order to find the average value of a function over a specified interval [0,b] you must integrate the function on that interval and divide by the interval length.

Can you formulate an equation which states these facts in terms of b and solve for b?
 

Related to Help with average value of a function

What is the average value of a function?

The average value of a function is the value that would represent the average height of the function's graph over a given interval. It is also known as the mean value of the function.

How do you find the average value of a function?

To find the average value of a function, you need to first find the definite integral of the function over the given interval. Then, divide the result by the length of the interval. The resulting value is the average value of the function.

Why is the average value of a function important?

The average value of a function helps to determine the overall behavior of the function over a certain interval. It can also be used to find the area under the function's graph, which has various real-world applications in fields such as physics and economics.

Can the average value of a function be negative?

Yes, the average value of a function can be negative. This occurs when the function has values below the x-axis, resulting in a negative definite integral. It is important to consider the direction of the function's graph when interpreting the average value.

What is the difference between average value and mean value of a function?

The terms "average value" and "mean value" are often used interchangeably when referring to the average value of a function. However, the term "mean value" is more commonly used in statistics to refer to the arithmetic mean of a set of numbers, while "average value" is more commonly used in calculus to refer to the mean value of a function over a given interval.

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