How to use rolles theorem for #f(x)= (x^3/3)- 3x# on the interval [-3,3]?
1 Answer
Rolle's theorem states that if a continuous differentiable function
For the function
we see that
#f(x)# is continuous and differentiable#f(-3)=0= f(3)#
Thus the conditions of Rolle's theorem are satisfied with
Since
(This could have been anticipated from the fact that in this case
Note that Rolle's theorem says that there is a
This can be easily seen from the graph
graph{x^3/3-3 x [-5, 5, -5, 5]}