1.Determine whether Rolle\'s Theorem can be applied to f on the closed interval
ID: 2849313 • Letter: 1
Question
1.Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
(Select all that apply.)
f(x) = 2 tan x, [0, ]
Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval
(a, b)
such that
f'(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
c =
2. Find the point on the graph of the function that is closest to the given point. (x,y)=(?,?)
f(x) =
x-7, (18,0)Explanation / Answer
1.Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
(Select all that apply.)
f(x) = 2 tan x, [0, ]
f is not continuous at x =pi/2
No, because f is not continuous on the closed interval [a, b].
2)distance of point (x,y) on y=sqrt(x-7) to (18,0)= D=sqrt[(x-18)2+y2]
distance is minimum if (x-18)2+y2 is minimum
g(x,y)=(x-18)2+y2
but y=sqrt(x-7)
==>g(x)=(x-18)2+(sqrt(x-7) )2
==>g(x)=(x-18)2+ (x-7)
minimum distance ==>g '(x)=0 ==>2(x-18)+(1-0)=0==>(x-18)=-1/2 ==>x=35/2
y=sqrt(x-7) ==>y=sqrt((35/2)-7) ==>y=sqrt(21/2)
(x,y)=(35/2 ,sqrt(21/2))
point on the graph of the function that is closest to the given point.is (x,y)=(35/2 ,sqrt(21/2))
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