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Use the graph of the derivative of f to locate the critical points x0 at which f has neither a local maximum nor a local minimum?


answer choices:

  1. x0 = a , b
  2. x0 = c , a
  3. x0 = a , b , c
  4. x0 = a
  5. none of a , b , c
  6. x0 = b
  7. x0 = b , c
  8. x0 = c

Use the graph of the derivative of f to locate the critical points x0 at which f has neither a local maximum nor a local minimum? answer choices: 1. x0 = a , b class=

Verified Answer :

syed514

Critical points are where the derivative is 0, i.e. where it crosses the x - axis

The Critical points lies where the derivative is 0, while it crosses the x-axis, SO, in this case the choice 3 looks like best answer for this.

Using the graph and the second derivative test, it is found that the critical point at which f has neither a local maximum nor a local minimum is \(x_0 = c\).

The critical points of a function f(x) are the values of \(x_0\) for which:

\(f^{\prime}(x_0) = 0\).

The second derivative test states that:

  • If \(f^{\prime\prime}(x_0) > 0\), \(x_0\) is a minimum point.
  • If \(f^{\prime\prime}(x_0) < 0\), \(x_0\) is a maximum point.
  • If \(f^{\prime\prime}(x_0) = 0\), \(x_0\) is neither a maximum nor a minimum point.

In this problem, the critical points are: \(x_0 = a, x_0 = b, x_0 = c\).

  • The graph is of the first derivative.
  • The derivative is the rate of change, thus, the second derivative is the rate of change of the first.

For each of the critical points:

  • At \(x_0 = a\), the derivative is increasing, thus \(f^{\prime\prime}(a) > 0\)
  • At \(x_0 = b\), the derivative is decreasing, thus \(f^{\prime\prime}(b) < 0\)
  • At \(x_0 = c\), the derivative "curves", so it is zero, which means that \(x_0 = c\) is neither a maximum nor a minimum.

A similar problem is given at https://brainly.com/question/16944025

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