Question

The graph of a twice differentiable functions with a relative minimum at (-1,-2) is shown to the right. Which of the following inequality statements is true?

Answer 1

I need to attach the graph.

Answer 2

I know the answer is
f(-1) < f ' (-1)< f " (-1) I am trying to figure out why this is true

Answer 3

the relative minimum is (-1,-2) so that means f ' (x) =0 since it has a horizontal tangent at that point so f '(-1)=0

Answer 4

minimum means decreasing to increasing

Answer 5

f(-1) is decreasing so I could assign negative to it

Answer 6

not sure what to assign to f " (-1)

Answer 7

never mind, I see if I make a sign chart using -2 or a point close to -2
that f " (-1) is positive since it is above the x axis so therefore it is positive

so negative < zero< positive
wonder if I did that correct?

Answer 8

@SolomonZelman

Answer 9

@ganeshie8