Question

Consider the function f(x) = x3 − 2x2 − 4x + 9 on the interval [−1, 3].

Find f '(x). f '(x) = 3x2−4x−4

Find the critical values. x =

Evaluate the function at critical values. (x, y) =

(smaller x-value)

(x, y) =

(larger x-value)

Evaluate the function at the endpoints of the given interval.

(x, y) =

(smaller x-value)

(x, y) =

(larger x-value)

Find the absolute maxima and minima for f(x) on the interval [−1, 3].

absolute maximum (x, y) =

absolute minimum (x, y) =

Answer #1

Consider the function f(x) = x^3 − 2x^2 − 4x + 7 on the interval
[−1, 3]. a) Evaluate the function at the critical values. (smaller
x-value) b) Find the absolute maxima for f(x) on the interval [−1,
3].

Find the absolute maximum and minimum values of f(x)=
−x^3−3x^2+4x+3, if any, over the interval
(−∞,+∞)(−∞,+∞).
I know it doesn't have absolute maxima and minima but where do
they occur? In other words x= ? for the maxima and minima?

question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x > 0
(a) Find the critical numbers of f. (Enter your answers
as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)
increasing
decreasing
question#2:
Consider the following function.
f(x) =
2x + 1,
x ≤ −1
x2 − 2,
x...

Find the local maximum and minimum values and saddle point(s) of
the function f ( x , y ) = f(x,y)=xe^(-2x2-2y2). If there are no
local maxima or minima or saddle points, enter "DNE."
The local maxima are at ( x , y ) = (x,y)= .
The local minima are at ( x , y ) = (x,y)= .
The saddle points are at ( x , y ) =

Find the absolute maximum and minimum values of the following
function on the given interval. If there are multiple points in a
single category list the points in increasing order in x value and
enter N in any blank that you don't need to use. f(x)=3(x2−1)3,
[−1,2]
Absolute maxima
x = y =
x = y =
x= y =
Absolute minima
x = y =
x = y =
x = y =

Consider the function f(x)=6x^2−4x+11, on the interval
, 0≤x≤10.
The absolute maximum of f(x) on the given interval is at x =
The absolute minimum of f(x) on the given interval is at x =

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...

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

Find the absolute maximum and absolute minimum values of
f(x)=x3+3x2−9x+1 on [-5,-1] , along with
where they occur.
The absolute maximum value is ? and occurs when x is ?
the absolute minimum value is ? and occurs when x is ?

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...

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