Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) g(θ) = 16θ − 4 tan(θ) θ =

,

,

Step-by-step explanation:

The critical numbers are found by the First Derivative Test, which consists in differentiating the function, equalizing it to zero and solving it:

Following equation needs to be solved:

The solution is:

Given that cosine is a periodical function, there are two subsets of solution:

,

,

answer: '

the distance between points l and m

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is