Question

The graph of f " (x) is given. Which of the following statements are true?

Answer 1

Ok I understand why 1 and 2 are true. I am needing help with the 3rd statement to determine if it is false or true.

Answer 2

It is true. Draw the line x = 1, which is a vertical line. You'll notice it goes right down the middle of the concave. Every value after that line is increasing.

Answer 3

It is false @ridoleor recall we are looking at the graph of the second derivative

Answer 4

III is false

Answer 5

so only 1 and 2 are true

Answer 6

@sourwing can you help me understand why 3 is false

Answer 7

remember f(x) is increasing if f'(x) > 0 and f(x) is decreasing if f'(x) < 0?

well we're trying to determine the graphing of f'(x).
so f'(x) is increasing if f''(x) > 0
and f'(x) is decreasing if f''(x) < 0

at x = 1 f''(x) < 0 so f'(x) is decreasing, not increasing

Answer 8

thanks