Question

verify rolle's theorem for sinx + cosx -1

Answer 1

We need an interval for that I would think O.o

Answer 2

yah , its given in d 1st quad

Answer 3

what is rolles theorem ? is it d same as intermediate value theorem ?

Answer 4

Nope. Rolle's theorem requires some sort of interval. For your function let's just make the interval [0,2pi]. Rolle's theorem says that if I take the f(left interval) and f(right interval), which in thise case would be f(0) and f(2pi), and these two end up being equal, then that means there's at least one number, c, inside of that interval where f ' (c) = 0

Answer 5

y is this so ? can u brief me about d proof ?

Answer 6

Your function isn't the easiest graphing wise, so let's just use cosx and the interval [0,2pi]. Basically if rolle's theorem applies, then there is some point in the interval where the slope is 0. So what Rolle's theorem requires is that if we plug in the end points into our function, we'll get the same answer. Well, if I plug in 0 into cos(x) I get 1. If I plug in 2pi into cos(x) I get. So they're the same. So now visually.




Basically, the ONLY way for two x-values to have the same y-value is if they are in a straight line or if they change directions.



SO basically, if the end points of an interval are the same value, you have to have some point in the interval where the derivative of that point = 0, meaning a slope of 0.