Find the critical points of the function and use the First Derivative Test to de

Question

Find the critical points of the function and use the First Derivative Test to determine whether the critical point is a local minimum or maximum (or neither). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(theta) = 12 sin theta + 12 Squareroot 3 cos theta on (0, 2pi) local minimum theta = times local maximum theta = times Determine the intervals on which the function is increasing or decreasing. (Enter your answers usinginterval notation. Enter EMPTY or for the empty set.) increasing decreasing

Explanation / Answer

Differentiating the function,

f'(x)=12cos(x)-12*root(3)*sin(x)

f'(x)=0;

tan(x)=1/root(3), x=30 degrees or pi/6.

Fuction is increasing in [0, pi/6), [pi/2,7*pi/6) and [3*pi/2,2*pi)

It is decreasing in [pi/6,pi/2], [7*pi/6,3pi/2]

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