Wednesday

April 16, 2014

April 16, 2014

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

- Mean-value theorem -
**MathMate**, Sunday, January 23, 2011 at 10:09amThe 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 1:25pmmean value theorem of x^3+x-6 with range of [0,2]

**Related Questions**

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 ...

Caluclus - [Mean Value Theorem] f(x)=-3x^3 - 4x^2 - 2x -3 on the closed interval...

math - verify that the function satisfies the hypotheses of the mean values ...

Calculus HELP!!! - Here is the graph. h t t p : / /goo.gl/PTc2I (spaces added at...

calculus - Find the values of c that satisfy the Mean Value Theorem for f(x)=6/x...

calculus - Find the values of c that satisfy the Mean Value Theorem for f(x)=6/x...

calculus - Verify that the hypotheses of the Mean-Value Theorem are satisfied on...

math - verify that the function satisfies the hypothesis of the mean value ...

calculus - verify that the function satisfies the hypothesis of the mean value ...