Just in case anyone was confused (as I was) how we know that h(a) and h(b) are equal to zero: At points a and b the curves intersect, meaning f(a) = g(a) and f(b) = g(b). Since h(a) = f(a) - g(a), h(a) = 0 and h(b) = f(b) - g(b), h(b) = 0
I know it's little late, but maybe this can help somebody else lol. You can write slope of a straight line as (change in y)/(change in x). In other words, (y1-y2)/(x1-x2). g(b) is a y value, g(a) is a y value and obviously a and b are x values. You can derive this from y=mx+b I think, but dont take my word on this last part.
Because g(x) is linear and his derivative is m where y=mx+b . That m is tanAlpha where Alpha is angle which g(x) makes with x-axis. That is simple to find, you just devide change in y and change in x.
Just in case anyone was confused (as I was) how we know that h(a) and h(b) are equal to zero: At points a and b the curves intersect, meaning f(a) = g(a) and f(b) = g(b). Since h(a) = f(a) - g(a), h(a) = 0 and h(b) = f(b) - g(b), h(b) = 0
tysm
Very interesting how without Rolle's Theorem this would not work!
Very much so.
The best proof video I’ve seen!
Good cooking! Keep it up
Super succinct and elegant! Thank you ~
The proof was helpful. Thanks a lot!
Super elegant proof beautiful
Very helpful, thank you!
Is it the best MVT proof on youtube?
Very neat, I understood perfectly! Thank you!
I got lost on why is g'(c) = [g(b)- g(a)]/[b - a]
I know it's little late, but maybe this can help somebody else lol.
You can write slope of a straight line as (change in y)/(change in x). In other words, (y1-y2)/(x1-x2).
g(b) is a y value, g(a) is a y value and obviously a and b are x values.
You can derive this from y=mx+b I think, but dont take my word on this last part.
Because g(x) is linear and his derivative is m where y=mx+b . That m is tanAlpha where Alpha is angle which g(x) makes with x-axis. That is simple to find, you just devide change in y and change in x.
elegant
❤
Cool😃
justin bieber