How do you verify that the function #f(x)=x^(3)-x^(2)-12x+4# satisfies the three hypotheses of Rolle's Theorem on the given interval [0,4] and then find all numbers c that satisfy the conclusion of Rolle's Theorem?
2 Answers
c=
Explanation:
Here f(0)= 4 and f(4)=4 Hence according to the Rolle's theorem there should be at least one c for which f'(c)=0.
To find c, get
x=
Check the hypotheses, then solve
Explanation:
Let's check the hypotheses of Rolle's Theorem:
(1)
(2)
(3)
So according to Rolle's Theorem
The roots of
Now
This leaves the solution