Question

1) Let f(x)=−x^3−12x^2−45x+2

a) Find the open interval(s) where the following function is concave upward or concave downward.

b)Find any inflection point(s).

c) Find absolute maximum and minimum values on [-5,5].

2) A fence must be built to enclose a rectangular area of 20,000 square feet. Fencing material costs $ 2.50 per foot for the two sides facing north and south and $3.20 per foot for the other two sides. Find the cost of the least expensive fence.

Answer #1

A fence must be built to enclose a rectangular area of
20,000ft2. Fencing material costs $1 per foot for the
two sides facing north and south and $2 per foot for the other two
sides. Find the cost of the least expensive fence.
The cost of the least expensive fence is $____.

A
fence must be built to enclose a rectangular area of 5000 ft^2.
Fencing material costs $4 per foot for the two sides facing north
and south and $8 per foot for the other two sides. Find the cost of
the least expensive fence.
The cost of the least expensive fence is $_

Determine where the graph of the function f(x) = 6x-√(4-x^2) is
concave upward and where it is concave downward. Also, find all the
inflection points of the function.

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.

f(x)=4x^3+9x^2−12x−3.
1.Find the interval(s) on which f is increasing.
Answer (in interval notation):
2. Find the interval(s) on which f is
decreasing.
Answer (in interval notation):
3. Find the local maxima of f. List
your answers as points in the form (a,b)
Answer (separate by commas):
4. Find the local minima of f.f. List
your answers as points in the form (a,b)
Answer (separate by commas):
5. Find the interval(s) on which f is concave
upward.
Answer (in interval notation):...

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

consider the function f(x) = x/1-x^2
(a) Find the open intervals on which f is increasing or
decreasing. Determine any local minimum and maximum values of the
function. Hint: f'(x) = x^2+1/(x^2-1)^2.
(b) Find the open intervals on which the graph of f is concave
upward or concave downward. Determine any inflection points. Hint
f''(x) = -(2x(x^2+3))/(x^2-1)^3.

1, Let f be a function such that f′′(x) =x(x+ 1)(x−2)^2. Find
the open intervals on which is concave up/down.
2. An inflection point is an x-value at which the concavity of a
function changes. For example, if f is concave up to the left of
x=c and f is concave down to the right of x=c, then x=c is an
inflection point. Find all inflection points in the function from
Problem 1.

Let
f(x)=((x+1)^2)/((x−1)^2)
(a) (8 pts) Find the intervals on which
f
increases and the intervals on which f decreases. Find
all the local maximum and minimum values of f
.
(b) Find the intervals on which f
is concave upward and concave downward. Find the inflection
points.

f(x)= 12x- x^3
1. where is the local min? x-value
2. where is fhe local max? x-value
3. what is the inflection point? (x and y)
4. for which interval is the graph "concave down"?
for
what interval is the graph concave up?

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