The graph of the second derivative of a function is shown below. State the x-coordinate(s) of the inflection points of f

Question

The graph of the second derivative  of a function  is shown below. State the x-coordinate(s) of the inflection points of f. If more than one value, separate your answers using commas.

GIVE ME THE EXACT X VALUE PLEASE

Answer 1

f has an inflection point at x = c when f"(c) = 0 AND when f"(x) changes sign at x = c.

f"(2) = 0 but f"(x) is positive on both sides of x = 2. So, there is not an inflection point when x = 2.

f"(4) = 0 and f"(x) is positive to the left of x = 4 and is negative to the right of x = 4. So, there is an inflection point when x = 4. ^

Answer 2

The second derivative is =0 at the possible inflection points. The second derivative changes sign at inflection points.

This second derivative graph shows = 0 (possible inflection points) at 2 and 4.

At an inflection point, the second derivative changes signs.

The graph shows that f''(x) changes signs at 4, but not at 2.

4 is the inflection point.