Question

1.) Use the second derivative test to find the relative extrema for f(x) = x4 – x3 - (1/2)x2 + 11. Also find all inflection points, discuss the concavity of the graph and sketch the graph.

Answer #1

Given f(x) = , f′(x) = and f′′(x) = , find all possible
x2 x3 x4
intercepts, asymptotes, relative extrema (both x and y values),
intervals of increase or decrease,
concavity and inflection points (both x and y values). Use these
to sketch the graph of f(x) = 20(x − 2)
.
x2

Find all relative extrema of the function. Use the
Second-Derivative Test when applicable. (If an answer does not
exist, enter DNE.)
f(x) = x4 − 4x3 + 7
relative maximum
(x, y)
=
relative minimum
(x, y)
=

For f(x) xe-x
( a) Find the local extrema by hand using the first derivative
and a sign chart. b) Find the open intervals where the function is
increasing and where it is decreasing. c) Find the intervals of
concavity and inflection points by hand. d) Sketch a reasonable
graph showing all this behavior . Indicate the coordinates of the
local extrema and inflections.

use the second derivative test to find the relative extrema if
any of the function f(x)=x+576/x

Use the second derivative to find the intervals where
f(x) = x4+8x3 is concave upward and concave
downward. Also find any points of inflection.

Find the relative extrema, if any, of the function. Use the
Second Derivative Test if applicable. (If an answer does not exist,
enter DNE.)
g(x) = x3 − 15x
(a) relative maximum (x,y) = ____
(b) relative minimum (x,y) = ____

Consider the function f(x) = −x3 + 4x2 + 7x + 1.
(a) Use the first and second derivative tests to determine the
intervals of increase and decrease, the
local maxima and minima, the intervals of concavity, and the
points of inflection.
(b) Use your work in part (a) to compute a suitable table of
x-values and corresponding y-values and carefully sketch the graph
of the function f(x). In your graph, make sure to indicate any
local extrema and any...

Find all relative extrema. Use second derivative test where
applicable for ?(?) = 2 sin ? + cos 2? ,[0, 2 ?].

(a) Using the second derivative test, find the relative/local
extrema (maxima and minima) of the function f(x) = −x 3 − 6x to the
power of 2 − 9x − 2.

Given the function g(x) = x3-3x + 1, use the first and second
derivative tests to
(a) Find the intervals where g(x) is increasing and
decreasing.
(b) Find the points where the function reaches all realtive
maxima and minima.
(c) Determine the intervals for which g(x) is concave up and
concave down.
(d) Determine all points of inflection for g(x).
(e) Graph g(x). Label your axes, extrema, and point(s) of
inflection.

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