Madoreo7
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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 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 class=

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irspow
The inflection points are when acceleration is equal to zero.  If the above graph is dy/dx, acceleration will be equal to zero when the slope of it is zero because that will mean velocity is constant at that point.

So if the graph of dy/dx has horizontal slopes at x=2 and 4, they are the x-coordinates of the inflection points of f(x).
Cricetus

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

According to the question,

For inflection point,

  • [tex]f''(x) =0[/tex]

and,

  • [tex]f''(x)[/tex]

changes its sign at the given point.

Given,

Slope of tangent to the graph of [tex]f'(x)[/tex] is 0 (zero) at,

  • [tex]x=2[/tex]
  • [tex]x =4[/tex]

then,

  • [tex]f''(2) =0[/tex],
  • [tex]f''(4) =0[/tex]

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

Thus the above answer is right.

Learn more:

https://brainly.com/question/16568436

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