Ap calc ab please help! thanks in advance
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.

Question

Ap calc ab please help! thanks in advance
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.

phi · Answer

concave down is $ \cap$ shaped
say f(x)= x^2  (which we know is a parabola with $ \cup $ shape
f'(x)= 2x  and f''(x)= 2.  

f'(x) > 0 means the slope of the tangent line is rising.  i.e. the function is rising

f'(c) =0 means c could be a max, min or inflection.

tmagloire1 · Answer

so in this case the answer is C since f'(c) =0 is the rel. max min inflect?

tmagloire1 · Answer

@phi

anonymous · Answer

The second statement is correct also