Answer:
0 < x < 1.5..
Step-by-step explanation:
The derivative is 12/(2x - 3)
12/2x - 3 > 0
The interval is 0 < 2x < 3
That is 0 < x < 1.5..
The function f(x)=6log_2(x) - 3 increasing at the greatest rate in the interval [1/8, 1/2]
Maxima and minima of a function are the extrema within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We have a function:
[tex]\rm f(x) = 6log_2x-3\\[/tex]
For the interval x ∈[2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
As we can see from the function value and its interval values the function increased at the greatest rate in the interval [1/8, 1/2]
Thus, the function f(x)=6log_2(x) - 3 increasing at the greatest rate in the interval [1/8, 1/2]
Know more about the maxima and minima here:
brainly.com/question/6422517
