Use the First Derivative Test to determine whether the critical point is a local min or max (or neither). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x)=(ln(2x)/8x)-7 (x>0)

Also determine the intervals on which the function is increasing or decreasing.

Step-by-step explanation:

Let be , the first and second derivatives of the function are, respectively:

Now, let equalise the first derivative to zero and solve the resulting expression:

This result is evaluated at the second derivative expression:

The critical value leads to a critical maximum and there are two intervals:

- Increasing

- Decreasing

The graphic of the function is presented below as attachment.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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4.

step-by-step explanation:

it have the same area.brainliest