Question

Given the function y = 2cos(x) - 1, use Calculus methods to determine the:

a) intervals of increase and decrease
b) local max and mins
c) intervals of concavity
d) inflection points

my answers:
a) decrease: [0,pi) increase: (pi,2pi]
b) local min: (pi,-3)
c) concave down:(-infinity, pi/2] U [3pi/2, infinity)
concave up: (pi/2, 3pi/2)
d) (pi/2,-1)
(3pi/2,-1)

Answer 1

All correct except:

for b) what about the local max's ?

d) disagree with your concavity properties. Look at the initial sketch of your graph
I assume you wanted everything in the domain from 0 to 2π
Then I see concave down for 0 < x < π/2 as well as 3π/2 < x < 2π
concave up for π/2 < x < 3π/2

Answer 2

y = 2 cos(x) - 1
y' = -2 sin x positive slope from pi to 2 pi agree, 0 at 0 and pi
y" = - 2 cos x positive (holds water) from pi/2 to 3 pi/2
agree so far, but sketch a graph