Question

1) find the absolute extrema of function f(x) = 2 sin x + cos 2x on the interval [0, 2pi]

2) is f(x) = tanx concave up or concave down at x = phi / 6

Answer #1

Find the absolute extrema of f(x, y) = cos x + cos y on the
diamond shaped region R with vertices(±π, 0) and (0, ±π).

Consider the function on the interval (0, 2π).
f(x) =
sin(x)/
2 + (cos(x))2
(a) Find the open intervals on which the function is increasing
or decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) Apply the First Derivative Test to identify the relative
extrema.
relative maximum
(x, y) =
relative minimum
(x, y) =

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 4. (A) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) (B) Apply the First Derivative Test to identify all
relative extrema.

f(x) = − cos(x^2 ) + 2 sin(x) [1,3.5]
1) find f'(x) and the roots on the given interval.
2) find all critical points of f(x) on the given interval.
3) find absolute max and min of f(x) on the given interval.

Find the absolute extrema of the function on the closed
interval
f(x)= 1 - | t -1|, [-7, 4]
minimum =
maximim =
f(x)= x^3 - (3/2)x^2, [-3, 2]
minimim =
maximim =
f(x)= 7-x, [-5, 5]
minimim =
maximim =

Find all local extrema and the intervals on which
f(x)=x+sin(2x), considered on the interval (-pi/2,pi/2) is
increasing or decreasing.?

f(x) = 10/cos-1(x). Use calculus to determine: a) all critical
values b) any local extrema c) any absolute extrema d) the
intervals where f is increasing/decreasing e) any points of
inflection rounded to the thousandths place f) intervals where f is
concave up/down

1. Find the area between the curve f(x)=sin^3(x)cos^2(x) and y=0
from 0 ≤ x ≤ π
2. Find the surface area of the function f(x)=x^3/6 + 1/2x from
1≤ x ≤ 2 when rotated about the x-axis.

Find the absolute maximum and minimum values of the function
f(x) = x^4-2x^2+1 on the interval [0,3]

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 2 (a) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) increasing Incorrect: Your answer is incorrect.
decreasing Incorrect: Your answer is incorrect. (b) Apply the First
Derivative Test to identify all relative extrema. relative maxima
(x, y) = Incorrect: Your answer is incorrect. (smaller x-value) (x,
y) = Incorrect: Your answer is incorrect. (larger x-value) relative
minima...

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