Can we find c that satisfies the conclusion of the mean value theorem? Calculus 1 tutorial

Can we find c that satisfies the conclusion of the mean value theorem? Calculus 1 tutorial

[viktorb]

im currently studying calc 2, i have a test this friday. i was absent for when we learned disk/washer & shell. i’ve watched a few of your videos and i really enjoyed them but im having a hard time understanding 1. when to use which method and 2. how to manipulate the formula to meet my needs (i.e finding the area between y=1 and y=x on the interval [0, 1] about y=0, x=0, y=1, & x=1)

thank you so much! your videos are incredibly helpful!!

[BloobleBonker]

Always a good idea to consider a graph of the function first!

[samuelhart]

Great video, as always. It may be worth specifying “real” solution in the question, or some naive student will proudly box in x = sqrt(2)*i+1 not realizing it makes no sense (I see myself falling down this trap).

[kaiudall]

I just noticed that bprp has a huge stack of marker boxes in the background 🤣

[guilhermerocha]

Great video and very good explanation. However, i believe a continuous function could also have a similar problem if theres a point where the function is not differentiable inside the interval. e.g. f(x) = |x| on any interval [a, b] such that a<0 and b>0

[swo.]

The function isn't discontinuous, it's undefined at x=1, you literally can't define f on [0;3]

It's rather defined on [0;1[u]1;3[ in which case the MVT doesn't apply for 0 and 3.