Sketch the graph of each function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. f ( x ) = x 2 + x − 2 2 x 2 − 2
Sketch the graph of each function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. f ( x ) = x 2 + x − 2 2 x 2 − 2
Solution Summary: The author calculates the increasing or decreasing region, relative extrema, asymptotes, concave up or down points of inflection and intercepts of the function.
Sketch the graph of each function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur.
1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative
maximum and minimum values of f.
(a) f(x) = x² - 2x²+3
(b) f(x) = (x+1)5-5x-2
(c) f(x) =
x2
x-9
2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f.
(a) f(x) = x - 2x²+3
(b) g(x) = x³- x
(c) f(x)=x-6x3 + x-8
3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test.
(a) f(x)=1+3x² - 2x3
(b) g(x) = 2x3 + 3x² - 12x-4
Find the
Soultion to the following dy
differential equation using Fourier in
transforms:
=
, хуо, ухо
according to the terms:
lim u(x,y) = 0
x18
lim 4x (x,y) = 0
x14
2
u (x, 0) =
=\u(o,y) =
-y
لو
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