# How do you find the point c in the interval #0<=x<=2# such that f(c) is equation to the average value of #f(x)=x^(2/3)#?

Solve the equation

So you need to solve

By signing up, you agree to our Terms of Service and Privacy Policy

To find the point ( c ) in the interval ( 0 \leq x \leq 2 ) such that ( f(c) ) is equal to the average value of ( f(x) = x^{2/3} ), we first need to calculate the average value of the function over the interval.

The average value of a function ( f(x) ) over the interval ( [a, b] ) is given by:

[ \text{Average value} = \frac{1}{b - a} \int_{a}^{b} f(x) , dx ]

In this case, ( a = 0 ) and ( b = 2 ). So, the average value of ( f(x) = x^{2/3} ) over the interval ( [0, 2] ) is:

[ \text{Average value} = \frac{1}{2 - 0} \int_{0}^{2} x^{2/3} , dx ]

We integrate this expression with respect to ( x ) over the interval ( [0, 2] ) and divide by the width of the interval, which is ( 2 - 0 = 2 ), to find the average value of the function.

Once we have the average value, we set ( f(c) ) equal to this average value and solve for ( c ). In other words, we find the value of ( c ) such that ( f(c) = \text{Average value} ) within the interval ( [0, 2] ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How can i solve this differencial equation? : #y'+x^2 y=x^2#
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #x= y^2# #x= y+2# rotated about the y-axis?
- What is a solution to the differential equation #dy/dt=e^t(y-1)^2#?
- How do you find the arc length of the curve #y = (x^4/8) + (1/4x^2) # from [1, 2]?
- What is the Volume of Revolution if the area bounded by the curve #y=x^2-4x# and the #x#-axis is is rotated about the #x#-axis?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7