Question

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- Consider the following. f (x) = x^5 − x^3+5 , − 1 ≤ x ≤ 1

(a) Use the graph to find the absolute maximum and minimum values of the function to two decimal places.

(b) Use calculus to find the exact maximum and minimum values

Answer #1

Consider: f(x)=ex-3x^2
Use the graphs of f' and f''.
1) What does the graph of f’ tell you about:
a) asymptotes for f? (exact values and why?)
b) intervals where f is increasing? where f is decreasing?
(exact values and why?)
c) x –values where f has a local minimum? local maximum?
absolute
minimum? absolute maximum? (exact values and why?)
2) What does the graph of f” tell you about:
a) concavity of f? (exact values and why?)
b) inflection...

Find the absolute maximum and absolute minimum of the
function
f(x) = x 3 − 6x 2 + 5
on interval [3, 6]
This problem is from chapter 4 of calculus early
transcendentals

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

The function f(x) = x^3 − 6x^2 − 15x + 1 has critical values x =
−1 and x = 5. Use calculus to determine whether each of the
critical values corresponds to a relative maximum, minimum or
neither.

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...

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.

Verify that the function
f(x)=(1/3)x3+x2−3x attains an absolute
maximum and absolute minimum on [0,2]. Find the absolute maximum
and minimum values for f(x) on [0,2].

1. Use f(x) as deﬁned below to complete parts (a) - (f). Draw an
accurate graph of the function on the grid below. Your graph should
be detailed with all applicable asymptotes and points of interest:
x and y intercepts, local and absolute minimum(s) (specify which on
graph), local and absolute maximum(s). Leave all numerical values
exact. f(x) = (x−1)√(4 + x) (a) domain:
(b) range:
(c) end behavior
lim f(x) =
x→−∞
lim f(x) =
x→∞
(d) critical values...

5- For f ( x ) = − x 3 + 7 x 2 − 15 x
a) Find the intervals on which f is
increasing or decreasing. Find the local (or absolute) maximum and
minimum values of f.
b) Find the intervals of concavity and the inflection
points.

Find the absolute maximum and minimum of the function f(x)=(2x2
+1)x4/3 for x∈[−1,8] Express your answers in simple exact form.

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