Question

1. Consider the equation below. (If an answer does not exist, enter DNE.)

f(x) = e^{2x} + e^{−x}

(b) Find the local minimum and maximum values of *f*.

local minimum value |

2. A particle is moving with the given data. Find the position of the particle.

a(t) = 13 sin(t) + 6 cos(t), s(0) = 0, s(2π) = 10

3. Find the area of the largest rectangle that can be inscribed in the ellipse

x^{2} |

a^{2} |

+

y^{2} |

b^{2} |

= 1.

4. Find the dimensions of the rectangle of largest area that can
be inscribed in an equilateral triangle of side *L* if one
side of the rectangle lies on the base of the triangle.

height:

5.

The top and bottom margins of a poster are each 12 cm and the
side margins are each 8 cm. If the area of printed material on the
poster is fixed at 1536 cm^{2}, find the dimensions of the
poster with the smallest area.

width | cm |

height | cm |

6. A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

(b) How much wire should be used for the square in order to
minimize the total area?

Answer #1

Consider the equation below. (If an answer does not exist, enter
DNE.)
f(x) =
x4 − 8x2
+ 7
(b) Find the local minimum and maximum values of f.
(c) Find the interval on which f is concave up. (Enter
your answer using interval notation.)
(d) Find the interval on which f is concave down.(Enter
your answer using interval notation.)

Consider the equation below. (If an answer does not exist,
enter DNE.)
f(x) = x^7ln(x)
(a) Find the interval on which f is increasing. (Enter your
answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up....

Consider the equation below. (If an answer does not exist,
enter DNE.)
f(x) = x^4− 50x^2 + 7
(a) Find the interval on which f is increasing. (Enter your
answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection points.
(x, y) =
(smaller x-value)
(x, y) =
...

Consider the following function. (If an answer does not exist,
enter DNE.)
f(x) = 1 +
5
x
−
3
x2
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.)
(e) Find the interval where the function is concave down. (Enter
your answer using interval notation.)
(f) Find the inflection point.
(x, y) =

Consider the function below. (If an answer does not exist, enter
DNE.)
f(x) = 1/2x^(4) − 4x^(2) + 3
(a)
Find the interval of increase. (Enter your answer using interval
notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b)
Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c)
Find the inflection points.
(x, y) = (smaller x-value)
(x, y) =...

Consider the function below. (If an answer does not exist, enter
DNE.)
h(x) = (x
+ 1)9 − 9x − 3
(a) Find the interval of increase. (Enter your answer using
interval notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b) Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c) Find the inflection point.
(x, y) =
Find the interval...

Consider the function below. (If an answer does not exist, enter
DNE.)
g(x) = 250 +
8x3 +
x4
(a) Find the interval of increase. (Enter your answer using
interval notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b) Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c) Find the inflection points.
(x, y)=(smaller x-value)
(x, y)=(larger x-value)
Find the...

Consider the following. (If an answer does not exist, enter
DNE.)
f '(x) =
x2 + x − 30
(a)
Find the open intervals on which f ′(x) is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
(−12,∞)
decreasing
(−∞,−12)
(b)
Find the open intervals on which the graph of f is
concave upward or concave downward. (Enter your answers using
interval notation.)
concave upward
concave downward
(c)
Find the x-values of the relative extrema of
f. (Enter...

MATH125: Unit 1 Individual Project Answer Form
Mathematical Modeling and Problem Solving
ALL questions below regarding SENDING A PACKAGE and PAINTING A
BEDROOM must be answered. Show ALL step-by-step calculations, round
all of your final answers correctly, and include the units of
measurement. Submit this modified Answer Form in the Unit 1 IP
Submissions area.
All commonly used formulas for geometric objects are really
mathematical models of the characteristics of physical objects. For
example, a basketball, because it is a...

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