If f(x) is continuous on [-4,4] such that f(-4)=11 and f(4)=-11 then

A. f(0)=0
B. lim x approaching 2 f(x)=8
C. Lim x approaching 3 f(x)=lim x approaching -3 f(x)
D. There is at least one value c in the interval [-4,4] such that f(c)=8
E. it is possible that f(x) is not defined at x=o

Question

If f(x) is continuous on [-4,4] such that f(-4)=11 and f(4)=-11 then

A. f(0)=0
B. lim x approaching 2 f(x)=8  
C. Lim x approaching 3 f(x)=lim x approaching -3 f(x)
D. There is at least one value c in the interval [-4,4] such that f(c)=8
E. it is possible that f(x) is not defined at x=o

anonymous · Answer

Is this a multiple choice

anonymous · Answer

Yes

anonymous · Answer

If so the answer is D) 
By Intermediate Value Theorem you know that if the function is continuous on 
$$y \in [-11,11]$$
So it has to pass through 8.

anonymous · Answer

What is the intermediate value theorem

anonymous · Answer

http://www.mathsisfun.com/algebra/intermediate-value-theorem.html