Question

f(theta)=2cos(theta)+cos^2 (theta)
0 is less than equal to theta is less than equal to 2pi

a. find the intervals of increase and decrease (use interval notation)

b. find local minimum and maximum values

c. find the inflection points
(x,y) smaller value
(x,y) larger value

d. find the intervals where the graph is concave upward and downward (use interval notation)

Answer 1

this involves evaluating 1st and 2nd derivatives
what is
f'(x)
f''(x)

Answer 2

local min/max occur when
f'(x) = 0

function increases when
f'(x) > 0

function decreases when
f'(x) < 0

inflection points occur when
f''(x) = 0

function is concave up when
f''(x) > 0

function is concave down when
f''(x) < 0

Answer 3

would it be
f ' (x) = -2sin (theta) (cos(theta) +1)
f '' (x) = 2 sin^2 (theta) - 2 cos (theta) (cos(theta)+1) ??

Answer 4

Im still not getting the right answers