If f(x)=1/x, then f(x) is always concave up for xer?

Question

True or False? explain

Answer 1

f(x) = x^-1
f'(x) = -x^-2
f"(x) = 2 x^-3 = 2/x^3
This is + for +x and - for -x so sometimes concave up and sometimes concave down