Suppose p(x) is a twice-differentiable function such that p(1) = 3, p'(1) = 0, and p”(1) = -2. Which of the following is true?

Question

there is a relative maximum at p(1) = 3

there is a relative minimum at p(1) = 3

there is a point of inflection at p(1) = 3

none of these are true

Answer 1

p'(1)=0 so max or min
p"(1) < 0, so concave down: a max

(A)