Rolle's theorem
Calculus
Level
3
Determine if all of the hypotheses of Rolle's theorem are satisfied on the stated interval
i) f(x) = (4-x^2)^0.5 on [-2, 2]
ii)f(x) = x^(2/3) - 1 on [-1, 1]
iii) f(x) = sin(x^2) on [0, (pi)^0.5]
i and ii
ii and iii
i and iii
All of the above
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
i) f'(x)= (\frac{x}{(4-x^2)^0.5}) = 0
x=0 which is a point on the interval
ii) f'(x) = 2\3(x)^0.666 = 0
but in x can't be equal to 0 but it will be something that has decimels iii) f'(x) = 2xcos(x^2) = 0
we know that when x= pi\2 cos becomes 0 so x will be (pi\2)^0.5 which is a point on the interval