Question

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

Answer 1

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.

Answer 2

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