Graphing

Consider the equation below.
f(x) = 2(cos(x))2 - 4sin(x)
0 ≤ x ≤ 2
(a) Find the interval on which f is increasing.
(b) Find the local minimum and maximum values of f.
(min)
(max)

(c) Find the inflection points. (Order your answers from smallest to largest x-value.)
( , ) (smaller x value)
( , ) (larger x value)

Find the interval on which f is concave up.
Find the intervals on which f is concave down.

Quote:

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Originally Posted by sheva2291

Consider the equation below.
f(x) = 2(cos(x))2 - 4sin(x)
0 ≤ x ≤ 2
(a) Find the interval on which f is increasing.
(b) Find the local minimum and maximum values of f.
(min)
(max)

(c) Find the inflection points. (Order your answers from smallest to largest x-value.)
( , ) (smaller x value)
( , ) (larger x value)

Find the interval on which f is concave up.
Find the intervals on which f is concave down.

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set f'(x) = 0 to find critical values in the given interval

find the sign of f'(x) between critical values to whether f(x) is increasing or decreasing

set f''(x) = 0 to find critical values in the given interval

find the sign of f''(x) between critical values to whether f(x) is concave up or down ... inflection points occur where concavity changes.