Question

Answer the following questions for the function
f(x)=x√(x^(2)+25)
defined on the interval [−5,7].

a.) f(x) is concave down on the interval .

b.) f(x) is concave up on the interval .

c.) The minimum for this function occurs at x= .

d.) The maximum for this function occurs at x= .

Answer 1

a) vertical asymptotes
x0 where f(x) does not exist and f(x)->infinity,x->x0 so x^2-1=0 then x=1, x=-1
b) we must find f"
f"=2x(x^2+3)/(x^2-1)^3
f"=0 then x=0
f"(2)>0 but f"(1/2)<0
so f(x) cant be concave up on the given region

c) points of reflection f"=0 so x=0