Let g be a twice differentiable function, and let g(4)=-2, g^(')(4)=0, and g^('')(4)=6. What occurs in the graph of g at the point (4,-2) ? Choose 1 answer: (A) (4,-2) is a minimum point. (B) (4,-2) is a maximum point. (C) There's not enough information to tell.

Given Information: We are given that g is a twice differentiable function, and we have the following information about g and its derivatives at x = 4: - g(4) = -2 - g'(4) = 0 - g''(4) = 6 The value of g(4) = -2 tells us the y-coordinate of the point on the graph of g at x = 4. The value of g'(4) = 0 tells us that the slope of the tangent to the graph of g at x = 4 is zero, which means the graph has a horizontal tangent line at this point. This could indicate a local maximum, a local minimum, or a point of inflection. The value of g''(4) = 6 tells us the concavity of the graph at x = 4. Since g''(4) is positive, the graph of g is concave up at x = 4. This means that the point (4, -2) is a local minimum because the graph is shaped like a ＂U＂ around this point.

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Let
g be a twice differentiable function, and let
g(4)=-2,
g^(')(4)=0, and
g^('')(4)=6.
What occurs in the graph of
g at the point
(4,-2) ?
Choose 1 answer:
(A)
(4,-2) is a minimum point.
(B)
(4,-2) is a maximum point.
(C) There's not enough information to tell.

Let $g$ be a twice differentiable function, and let $g(4)=-2$ , $g^{\prime}(4)=0$ , and $g^{\prime \prime}(4)=6$ . $\newline$ What occurs in the graph of $g$ at the point $(4,-2)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $(4,-2)$ is a minimum point. $\newline$ (B) $(4,-2)$ is a maximum point. $\newline$ (C) There's not enough information to tell.

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Q. Let

g

be a twice differentiable function, and let

g(4)=-2

g^{\prime}(4)=0

, and

g^{\prime \prime}(4)=6

\newline

What occurs in the graph of

g

at the point

(4,-2)

\newline

Choose

1

answer:

\newline

(A)

(4,-2)

is a minimum point.

\newline

(B)

(4,-2)

is a maximum point.

\newline

Given Information: We are given that $g$ is a twice differentiable function, and we have the following information about $g$ and its derivatives at $x = 4$ :
- $g(4) = -2$
- $g'(4) = 0$
- $g''(4) = 6$

The value of $g(4) = -2$ tells us the $y$ -coordinate of the point on the graph of $g$ at $x = 4$ . The value of $g'(4) = 0$ tells us that the slope of the tangent to the graph of $g$ at $x = 4$ is zero, which means the graph has a horizontal tangent line at this point. This could indicate a local maximum, a local minimum, or a point of inflection.

The value of $g''(4) = 6$ tells us the concavity of the graph at $x = 4$ . Since $g$ $5$ is positive, the graph of $g$ is concave up at $x = 4$ . This means that the point $g$ $8$ is a local minimum because the graph is shaped like a ＂U＂ around this point.