Question

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?

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

second derivative negative means the function is concave down, aka leaning to the right

Answer 2

the first derivative is zero, so the tangent line is horizontal

Answer 3

so is it b?