The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is true?

The graph of f has a relative maximum at x = 0.
The graph of f has a relative minimum at x = 0.
The graph of f has an inflection point at x = 0.
The graph of f has an x-intercept at x = 0.

Question

The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is true?

 The graph of f has a relative maximum at x = 0.
 The graph of f has a relative minimum at x = 0.
 The graph of f has an inflection point at x = 0.
 The graph of f has an x-intercept at x = 0.

trisarahtops · Answer

@ganeshie8

trisarahtops · Answer

@Conqueror

trisarahtops · Answer

@IrishBoy123

trisarahtops · Answer

Hi :) is this kind of math familiar to u?

irishboy123 · Answer

none of them are strictly true, IMHO

but get a second opinion, i'm crap at maths

phi · Answer

I know  
y= -x^3  would give
y' = -3x^2
y'' = -6x
if we plot y= -6x, it "is continuous and decreasing with an x-intercept at x = 0"
and in this case, x=0 is an inflection point.