The figure below shows the graph of f ', the derivative of the function f, on the closed interval from x = -2 to x = 6. the graph of the derivative has horizontal tangent lines at x = 2 and x = 4.

find the x-coordinate of each of the points of inflection of the graph of f. justify your answer.

The x coordinates of point of inflection are "x = 2, 4". A further solution is provided below.

According to the question,

For inflection point,

and,

changes its sign at the given point.

Given,

Slope of tangent to the graph of is 0 (zero) at,

then,

and, slope changes its sign at x = 2, 4

Thus the above answer is right.

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