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Consider this function f(x)=6log2x-3. Over which interval is function f increasing at the greatest rate?

Sagot :

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]

What are maxima and minima?

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

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