Posted by **Erica** on Sunday, January 23, 2011 at 12:13am.

Given function f defined by f(x) = ( 1- x)³. What are all values of c, in the closed interval [0,3], that satisfy the conditions of the Mean Value Theorem?

- Mean-value theorem -
**MathMate**, Sunday, January 23, 2011 at 10:09am
The mean value theorem states that a continuous function between x=a and x=b will have at least one tangent parallel to the chord AB.

For f(x)=(1-x)³, the chord between 0 and 3 has a slope of

s=(f(3)-f(0))/(3-0)=-3

The value(s) of c required must satisfy

f'(c)=-3

So, differentiate with respect to x:

f'(x)=-3(1-x)²

and solve for

f'(x)=-3

to get

x=0 and x=2

Reject any solution that is not on the interval [0,3].

- Calc -
**Noran**, Monday, March 28, 2011 at 1:25pm
mean value theorem of x^3+x-6 with range of [0,2]

## Answer This Question

## Related Questions

- math - verify that the function satisfies the hypotheses of the mean values ...
- Caluclus - [Mean Value Theorem] f(x)=-3x^3 - 4x^2 - 2x -3 on the closed interval...
- mean value theorem - Show that the function f(x)=1-|x|, [-1,1] does not satisfy ...
- math - verify that the function satisfies the hypotheses of the mean values ...
- Math11 - Hello, I don't know how to do this, please help. Thank you. 1).Does the...
- Calc 1 - Does the function satisfy the hypotheses of the Mean Value Theorem on ...
- calc - Verify that the function satisfies the three hypotheses of Rolle's ...
- calculus - Verify that the hypotheses of the Mean-Value Theorem are satisfied on...
- calculus help - Does the function satisfy the hypotheses of the Mean Value ...
- Calculus Help Please!!! - does the function satisfy the hypotheses of the Mean ...

More Related Questions