SOLUTION: Answer the following questions for the function f(x)=xx2+4 defined on the interval [−4,6]. A. f(x) is concave down on the interval to B. f(x) is concave up on the int

Algebra ->  Test -> SOLUTION: Answer the following questions for the function f(x)=xx2+4 defined on the interval [−4,6]. A. f(x) is concave down on the interval to B. f(x) is concave up on the int      Log On


   

Question 1202119: Answer the following questions for the function
f(x)=xx2+4
defined on the interval [−4,6].
A. f(x) is concave down on the interval
to
B. f(x) is concave up on the interval
to
C. The inflection point for this function is at x=
D. The minimum for this function occurs at x=
E. The maximum for this function occurs at x=

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


What is xx2?   Do you mean +f%28x%29+=+x%5E2+%2B+4+ ?   If not, please correct and re-post. 





If you DID MEAN to write +f%28x%29+=+x%5E2+%2B+4+ then:



f'(x) = +2x+

f"(x) = +2+   <<< constant positive value so concave up "everywhere"

                           which of course includes [-4,6]



A.  It is not concave down at all on [-4,6]

B.  It is concave up on [-4,6]

C.  There is no inflection point on [-4,6] (or otherwise)

D.  The minimum is at x=0  (set f' = 0, solve for x)

E.  The maximum on [-4,6] occurs at x=6  (you check at the endpoints of the interval [-4,6]:  f(-4) = 20,   f(6) = 40.  Since no local maximums occur within the interval [-4,6] (rememmber it is concave up so you can only have a local minimum), there are no critical points to check on (-4,6) )