Calculus
posted by Lindsay .
Determine if Rolle's Theorem can be applied. If it can, find all values of c such that f'(c)=0.
f(x)=x^39x, [3,3]

f(x) is continuous over the domain. [3,3]
f(x) is differential.
f'(x) = 3x^{2} 9
f(x) has two equal value points on the independent axis.
f(3) = f(3) = 0
Therefore Rolle's Theorem Applies
.: Exists c such that f'(c)=0
Solve for c:
0 = 3c^{2}  9
... 
Ahh! That's the answer I had but I was doubting it because my partner got something else! Thanks!
Respond to this Question
Similar Questions

calc
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x)= x sqrt(x+21) , [21,0] If there is more than one solution … 
calc
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [1/2,1/2] Well according to Rolle's Theorem, … 
calculus
Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the three hypotheses of Rolle’s theorem on the interval [0,3]. Then find the values of c on the interval [0,3] that are guaranteed by Rolle’s theorem. Give your answer … 
Math
Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that … 
Calculus
1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[4,2]. If Rolle's Theorem can be applied, … 
Calculus
1. Determine whether Rolle's Theorem applied to the function f(x)=((x6)(x+4))/(x+7)^2 on the closed interval[4,6]. If Rolle's Theorem can be applied, find all numbers of c in the open interval (4,6) such that f'(c)=0. 2. Determine … 
calculus
determine whether the mean value theorem can be applied to f on the closed interval [a,b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a,b) such that f(c) =f(b)  f(a) / b  a 
Calculus
Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3)  1 [8,8] I plugged in both values … 
Calculus
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x)= x^210x+3, [0,10] 
calculus
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x^2/3 − 2, [−8, 8] 1) Yes, Rolle's Theorem can be applied. 2)No, because f is not continuous on the closed …