Let
𝑔
be a function with domain
𝑅
.

Given the following table:

x g(x) g'(x)
1 9 -3
2 7 8
3 11 6
4 5 -3.5

What is
𝑑
𝑑
𝑥
3
𝑔
(
𝑥
)
evaluated at
𝑥
=
2
?

Enter you answer in decimal form, and round to 2 decimal places if needed (e.g. enter 0.1 as 0.1, enter 0.1234 as 0.12 or 0.13).

Question

Let 
𝑔
 be a function with domain 
𝑅
.

Given the following table:

x	g(x)	g'(x)
1	9	-3
2	7	8
3	11	6
4	5	-3.5

What is 
𝑑
𝑑
𝑥
3
𝑔
(
𝑥
)
 evaluated at 
𝑥
=
2
 ?

Enter you answer in decimal form, and round to 2 decimal places if needed (e.g. enter 0.1 as 0.1, enter 0.1234 as 0.12 or 0.13).

BlackTom AI · Accepted Answer

To determine d/dx [g(x)] at x = 2, we should consult the derivative column provided in the table for the corresponding x-value.
Looking at x = 2, the table lists g'(2) = 8. This value directly represents the instantaneous rate of change of g at x = 2, i.e., the derivative at that point.
Since the problem asks for the derivative evaluated at x = 2, the relevant quantity is g'(2), which the table provides as 8.
For clarity, note that the derivative g'(x) is defined as the slope of the tangent to the graph of g at x, so reading off g'(2) from the table is the standard way to obtain the requested derivative value without additional calculation.
The absence of any other conditions or instructions implies we rely solely on the tabulated derivative value at the specified x, which is the direct answer to the query.

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