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4 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 ? 9x2 ? 108x + 2, [?3, 4]

1 answer:

4 0

Assuming the question marks are minus signs
to find max, take derivitive and test 0's and endpoints

take derivitive
f'(x)=18x²-18x-108
it equal 0 at x=-2 and 3
if we make a sign chart to find the change of signs
the sign changes from (+) to (-) at x=-2 and from (-) to (+) at x=3
so a reletive max at x=-2 and a reletive min at x=3

test entpoints

f(-3)=83
f(-2)=134
f(3)=-241
f(4)=-190

the min is at x=3 and max is at x=-2

You might be interested in

Solve the following equation: 96= -6( -4-3y)<br> a. y=2<br> b.y=4<br> c.y= -2<br> d. y=6

tankabanditka [31]

96 = -6 * (-4 - 3y) <== It's easiest to solve when the y is on the right
   ↓
-6 * (-4 - 3y) = 96      <== Multiply the -6 by everything inside the
         parentheses
  <span>↓</span>
   24 + 18y = 96 <== Subtract the 24 from both sides
↓
18y = 72 <== Divide both sides by 18
↓
y = 4

The correct answer is choice B. y = 4.
Hope that helped =)

3 0

4 years ago

Read 2 more answers

ASAP JUST ANSWER THX

DochEvi [55]

Answer:

The second one

Step-by-step explanation:

Y=11/4x+3/2

4 0

3 years ago

An estate valued at $510,000 is to be distributed among the wife, 2 children, and 3 grandchildren. The children each receive two

4vir4ik [10]

Each grandchild receives x.

Each child receives 2 times as much as a grandchild, so each child receives 2x.

The wife receives 5 times as much as a child, so the wife receives 5 * 2x = 10x.

There is 1 wife: 10x

There are 2 children: 2 * 2x = 4x

There are 3 grandchildren: 3x

Total: 10x + 4x + 3x = 17x

17x = 510,000

x = 30,000

Answer:

Each grandchild gets $30,000.

Each child gets 2 * $30,000 = $60,000.

The wife gets 10 * $30,000 = $300,000.

6 0

3 years ago

I need the parent function and the transformation with some explanation, thank you.

True [87]

Answer:

parent: y = x²
transformed: y = -3x² +4

Step-by-step explanation:

You have correctly recognized that the function is quadratic, so has parent function y = x².

You may notice that the function drops by 3 units when x increases or decreases by 1 unit from the vertex. That factor (-3) is the vertical scale factor in the transformed function ...

f(x) = a(x -h)² +k

where "a" is the vertical scale factor and (h, k) is the location of the vertex of the transformed function.

We note that the graphed function has its vertex at (h, k) = (0, 4), so the complete transformed function with a=-3, h=0, k=4 is ...

f(x) = -3x² +4

7 0

3 years ago

Two families are planning a trip to Disney. The Smith family bought tickets for 2 adults and 3 children for $557. The Jones fami

emmainna [20.7K]

<em>An adult ticket costs $205 and a child ticket costs $49.</em>

<h2>Explanation:</h2>

Hello! Recall you have to write complete questions in order to find exact answers. Here I'll assume the complete question as:

<em>Two families are planning a trip to Disney. The Smith family bought tickets for 2 adults and 3 children for $557. The Jones family bought tickets for 2 adults and 1 child </em><em>for $459</em><em>. How much does and adult and child ticket cost?</em>

To solve this problem, we need to write a system of linear equations in two variables. So, we know some facts:

Two families are planning a trip to Disney.
The Smith family bought tickets for 2 adults and 3 children for $557.
The Jones family bought tickets for 2 adults and 1 child for $459.

Let:

$x:Cost \ of \ ticket \ per \ adult \\ \\ y: Cost \ of \ ticket \ per \ child$

For the Smith family:

Cost for the 2 adults:

$2x$

Cost for the 3 children:

$3y$

Total cost:

$2x+3y=557$

For the Jones family:

Cost for the 2 adults:

$2x$

Cost for the 1 child:

$y$

Total cost:

$2x+y=459$

So we have the following system of linear equations:

$\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}2x+3y=557\\2x+y=459\end{array}\right.$

Subtracting (2) from (1):

$\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}2x+3y=557\\-(2x+y=459)\end{array}\right. \\ \\ \\ \begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}2x+3y=557\\-2x-y=-459\end{array}\right. \\ \\ \\ (2x-2x)+(3y-y)=557-459 \\ \\ 2y=98 \\ \\ y=49 \\ \\ \\ Finding \ x \ from \ (1): \\ \\ 2x+3(49)=557 \\ \\ 2x=557-147 \\ \\ 2x=410 \\ \\ x=205$

Finally, <em>an adult ticket costs $205 and a child ticket costs $49.</em>

<h2>Learn more:</h2>

System of linear equations: brainly.com/question/13799715

#LearnWithBrainly

3 0

4 years ago