Question

Consider the function: f(x)=7x^5−ax^7 where a is a constant. Find the value of a such that f(x) has a local minimum at x=1 ? Which of the following lists contains this value of a ?

- 3, 4, 5 , 6, 7

-20, 21, 22 , 23, 24

-29, 30, 31, 32, 33

- -7,-6,-5, -4, -3

Answer #1

Since function has local maximum at , function has critical point at

Therefore

The list containing value of a is given by

- 3, 4, 5 , 6, 7

-----------------------------------------------------------------

1. Find the constants a and b so that the function f is
continuous, where
f(x) =(ax^2 + bx if x <=1 or x > 2; (7x+4) 3 if 1 < x
<= 2

Find the instantaneous rate of change of the function
f(x)=7x^3+7 at x=5. Show your work.

Given the function f (x, y) = ax^2
2 + 2xy + ay.y
2-ax-ay. Take
for a an integer value that is either greater than 1 or less
than -1, and
then determine the critical point of this function. Then
indicate whether it is
is a local maximum, a local minimum or a saddle point.
Given the function f (x, y) = ax^2 +2 + 2xy + ay^2-2-ax-ay.
Take
for a an integer value that is either greater than 1...

53) Consider the function f(x) whose second derivative is
f''(x)=7x+5sin(x). If f(0)=2 and f'(0)=4, what is f(3)f?

Person
number
X
Value
Y
Value
Person number
X
Value
Y
Value
Person number
X
Value
Y
Value
1
24
30
11
39
42
21
21
27
2
42
53
12
60
65
22
33
29
3
20
27
13
34
40
23
25
27
4
31
30
14
24
26
24
22
25
5
22
24
15
51
57
25
28
33
6
46
47
16
80
83
26
34
40
7
52
60
17
28
27
27
53...

The function f(x) = x^3+ax^2+bx+7 has a relative extrema at x =
1 and x = -3.
a.) What are the values of a and b?
b.) Use the second derivative test to classify each extremum as
a relative maximum or a relative minimum.
c.) Determine the relative extrema.

Consider the function in x,y where f(x,y) =
7.47x2 + 2.47xy + 8.05y.
Find the x value corresponding to a local minim or
maximum.

(1 point) Find the degree 3 Taylor polynomial T3(x) of
function
f(x)=(7x+67)^(5/4)
at a=2
T3(x)=?

Find the degree 3 Taylor polynomial T3(x) of function
f(x)=(7x−5)^3/2 at a=2. T3(x)=

Find the equation of the tangent line to the function f(x) =
ln(7x) at x=4.
(Use symbolic notation and fractions where needed. Let y = f(x)
and express the equation of the tangent line in terms of y and
x.)
equation:

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