Start learning today, and be successful in your academic & professional career. Start Today!

Loading video...

This is a quick preview of the lesson. For full access, please Log In or Sign up.

For more information, please see full course syllabus of Calculus AB

For more information, please see full course syllabus of Calculus AB

0 answers

Post by Angela Zhang on December 7, 2014

John, you are very cute! I like you <3

0 answers

Post by Yu Han on July 24, 2014

For example 1, how can you tell if it met these two conditions?

0 answers

Post by Justin Powell on February 10, 2014

Just for clarity:

The Mean Value Theorem says that if a function f(x) is continuous

and differentiable between two intervals x=a and x=b,

then solving the function for these two values will give

the coordinates {a,f(a)} and {b,f(b)}.

Now if you draw a line between these two points, the slope will be:

(f(b)-f(a))/(b-a) which is the rise over the run.

The Mean Value Theoem states that at some point, {c,f(c)},

on the graph of the function between the intervals x=a an x=b,

the derivative or slope must be equal to (f(b)-f(a))/(b-a) at least once.

So the derivative of f(x) at x=c is equal to:

f'(c)=(f(b)-f(a))/(b-a)

In the last example:

the slope between the coordinates {-1,-1} and {5,125} equals

126/6 = 21=f'(c)=3c^2 c=sqrt(7).

At f(sqrt7) the slope of the curve of the graph is

parallel to the line between {-1,-1} and {5,125}.

also for the MVT, f'(c)=0 is only true when f(a) and f(b)

are equal (Rolles theorem).

Sorry for overclarifying, but the video left out some

key points.

1 answer

Last reply by: Andrew Mu

Mon Jan 6, 2014 8:30 AM

Post by Willie Wang on January 13, 2013

AT Example 4, why c cannot be negative sqr(7)ï¼Ÿ

1 answer

Last reply by: Johnny Zamora

Fri Jan 10, 2014 2:58 AM

Post by James Xie on December 17, 2012

What exactly does c stand for? Is it the Instant Rate Of Change (IROC?

0 answers

Post by Ryan Menezes on November 18, 2012

That's exactly what i want to know......

1 answer

Last reply by: Siyun Liu

Sat Jan 24, 2015 6:57 PM

Post by Steve Denton on October 18, 2012

At 5:00, what happened to the 1/2 in front of (c-1)^-1/2?

rewritten then 1/ (2 sq rt (c-1))?????