X) = 3 ln(x)
g(x=2) = 3 ln(2)
g(x=4) = 3 ln(4) = 3 ln(22) = 6 ln2
We have two ordered pairs:
(x,3 ln(2)) and (4,6 ln(2))
The average rate of change is the slope (m) of the secant line connecting the two points:
m = (6 ln2 - 3 ln2)/(4-2) = 3ln(2)/2 ≅ 1.04
5/8-5/12(3-1/4)+2/3=5/8- 5/12 * (12/4-1/4)+2/3=
5/8- 5/12 * (11/4) +2/3=
5/8- 55/48 + 2/3=
30/48 - 55/48 + 32/48=
-25/48 +32/48=
7/48
Your answer is B.
The equation is separable, so solving it is trivial:

Integrating both sides gives

Given
and
, we find


so the answer is E.
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Were the problem? i don’t see it.