MATH 1A Lecture Notes - Lecture 19: Mean Value Theorem
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Math 1a lecture 19 4. 2 mean value theorem. Then, there exists a c (a ,b) such that: f " (c)= f (b) f (a) b a f (b) f (a) b a and differentiable. = average value of the f " (x) on (a,b) For example, let x correspond to ttime and function of time. f (x) correspond to distance as a f (b) f (a) b a. = average velocity or average rate of change in. Since the velocity at x is average velocity is attained. f " (x ) , the theorem says that at some point x=c , the. Notice here that the tangent line at x=c is parallel to the slope from a to b , which represents the average velocity. So is equal to the average velocity. f "(c) This is an example of an existence theorem ; it guarantees that a c with stated properties exists somewhere.
shows the distance travelled by the car in meters and time 
in sec. The figure shown below is a parabola which is continuous and differentiable between 
. It goes through points 
, 
and 
. Determine the point 
where the instantaneous velocity is equal to average velocity by Mean Value Theorem.