MATH 1A Lecture 19: MATH 1A – Lecture 19 – 4.2 Mean Value Theorem.docx
Document Summary
Math 1a lecture 19 4. 2 mean value theorem. Let f ( x ) be continuous on. Then, there exists a c (a , b) such that: f " (c)= f (b) f (a) b a f (b) f (a) b a differentiable. = average value of the f " ( x) on (a,b) , if f ( x) is continuous and. 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)
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.