Question

Guys, please Help me. I give medals.

Which one of the following statements is true?

-If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b).

- If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b).

-If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x).

-None of these are true.

Answer 1

@ganeshie8 @dan815

Answer 2

@satelitte

Answer 3

@jim_thompson5910 @phi

Answer 4

B is the answer. because c is wrong because if you have a slope of zero, it can be a max but it also can be a min. a is wrong because when you have concavity up, the f''x must be greater than zero and positive.

Answer 5

`If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x)`

there could be a relative min or a saddle point. So this statement is false.

Answer 6

`If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b)`

false. f(x) is concave up if the second derivative is positive

Answer 7

`If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b)`

this is definitely true