# Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x)=2-x^2 on the interval [0,√2). If so, find the x-coordinates of the point(s) guaranteed by the theorem

a) No, the Mean Value Theorem for Integrals does not apply
b) Yes, x=4/3
c) Yes, x= √5/3
d) Yes, x=√(2/3)

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. integral = 2 x - x^3/3 at sqrt 2 - at 0
= 2 * 2^.5 - 2^(1.5)/3 - 0

length of rectangle = 2^.5
so
y * [ 2^.5 ] = 2 * 2^.5 - 2^(1.5)/3
y * [ 2^.5 ] = 2 * 2^.5 - 2^.5 *2 /3
y * [ 2^.5 ] = 2 * 2^.5 [ 1-1/3)
y * [ 2^.5 ] =(4/3) (2^.5)
y = 4/3
where is that?
2-x^2 = 4/3
x^2 = 2/3
d

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### math

Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the

2. ### math

Determine if the Mean Value Theorem for Integrals applies to the function f of x equals the square root of x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.

3. ### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = √x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. a) No, the theorem does not apply b)

4. ### Calculus

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Enter your answers as a comma-separated list.) f(x) = x^4, [0, 4]

1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

2. ### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 - 9x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. I think one point is zero.

3. ### Calculus

Consider f(x)=x^2-2x-3 (a). Find the average value of f(x) on the interval [0,3] (b). Find the value(s) of C in [0,3] guaranteed by the Mean Value Theorem for Integrals. Any help is appreciated!

4. ### Calc

Find the Value(s) of C guaranteed by the Mean Value Theorem for Integrals for f(x) =x^3 in the interval [0,3]

In this problem you will use Rolle's theorem to determine whether it is possible for the function f(x) = 8 x^{7} + 7 x - 13 to have two or more real roots (or, equivalently, whether the graph of y = f(x) crosses the x-axis two or

2. ### Math

Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f

3. ### math

Consider the function f ( x ) = 3x^3 − 3x on the interval [ − 4 , 4 ] . Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one c in the open interval ( −

4. ### Calculus

The function f is continuous on the closed interval [1,7] and has values in the table below x f(x) 1 10 4 30 6 40 7 20 Usinf the subintervals [1,4] [4,6] [6,7] what is the trapezoidal apporx. of the integral from 1 to 7 of f(x)dx?