Question

Determine whether Rolle's theorem applies on the given interval and tell why. find all values of c in the open interval (a,b) that f'(c)=0

f(x)=2-|x-4|, [1,6]

Answer 1

In my view, you can't apply it because that function is not differentiable at x=4...
Rolle's theorem states that it must be differentialble at all points in [a,b]

Answer 2

so then sense it is a absolute value and that makes it not continuous on the interval it is not differentiable

Answer 3

Yes, it has what is called a cusp, if I recall, whih is not differentiable.

Answer 4

it is continuous, but not differentiable

Answer 5

and the derivative would be 1 if i say

Answer 6

Ah, yah, continuous but not diff. Syderitic is absolutly correct there.

Answer 7

if you approach x=4 from the right you will get -1 fot the slop, from the left you will get 1

Answer 8

https://www.desmos.com/calculator/59z3jijhi9

Answer 9

that is what i get, so then even if it is not differentiable would i still need to find the derivative, then set it to zero

Answer 10

To be honest, you can't. There is a maxima, but it is at a point that is not differentiable and therefore has no derivative.

Answer 11

thats the last part i needed thank you

Answer 12

derivative in that point can be any value from [-1,1], or should i say you can draw a tangential line with any of those slopes...but that derivative is not defined => no point