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Andru [333]
2 years ago
11

The function f is continuous on the interval (0,16), and f is twice differentiable except at x=5 where the derivatives are undef

ined. Information about the first and second derivatives of f for values of x in the interval (0,16) is given in the table above. At what values of x in the interval (0,16) does the graph of f have a point of inflection?.
SAT
1 answer:
Oliga [24]2 years ago
7 0

Using it's definition, it is found that the function f(x) has a point of inflection at:

A. x = 8 only.

<h3>What are the points of inflection of a function?</h3>
  • The critical points of a function are the <u>values of x</u> for which:

f^{\prime\prime}(x) = 0

  • Additionally, there has to be a change in the sign of f^{\prime\prime}(x)

Researching the problem on the internet, it is found that:

  • For 0 < x < 5, f^{\prime\prime}(x) > 0.
  • For x = 5, f^{\prime\prime}(x) is undefined.
  • For 5 < x < 8, f^{\prime\prime}(x) < 0.
  • For x = 8, f^{\prime\prime}(x) = 0.
  • For 8 < x < 12, f^{\prime\prime}(x) > 0.
  • For x = 12, f^{\prime\prime}(x) = 0.
  • For 12 < x < 16, f^{\prime\prime}(x) > 0.

The two conditions, f^{\prime\prime}(x) = 0 and a change in the signal of f^{\prime\prime}(x) are only respected at x = 8, which is the lone inflection point.

You can learn more about points of inflection at brainly.com/question/10352137

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To know the species which the same number of protons as Fe³⁺, we need to obtain the <em>atomic number of the elements on the periodic table</em> :

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Learn more :brainly.com/question/18631164

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