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Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont

Neko [114]

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

$f(x) = x^{3}-9\cdot x^{2}+ 3$ , $2 \leq x \leq 12$

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

$f'(x) = 3\cdot x^{2}-18\cdot x$

$3\cdot x^{2}-18\cdot x = 0$

$3\cdot x \cdot (x-6) = 0$ (Eq. 1)

As we can see, only a solution is a valid critical value. That is: $x = 6$

Second, we determine the second derivative formula and evaluate it at the only critical point:

$f''(x) = 6\cdot x -18$ (Eq. 2)

x = 6

$f''(6) = 6\cdot (6)-18$

$f''(6) =18$ (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

$f(2) = 2^{3}-9\cdot (2)^{2}+3$

$f(2) = -25$

x = 6

$f(6) = 6^{3}-9\cdot (6)^{2}+3$

$f(6) = -105$

x = 12

$f(12) = 12^{3}-9\cdot (12)^{2}+3$

$f(12) = 435$

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

6 0

3 years ago

Help on this problem

GREYUIT [131]

0.77(13.50×40)= 415.8
The answer is $415.8

Hope this helps :)

6 0

3 years ago

I need fast help with step by step<br> <img src="https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_1%20%7B%5Cfrac%7B3x-1%7D%7Bx%2B1%7D

Ganezh [65]

Answer:

1.38 to the nearest hundredth.

Step-by-step explanation:

Dividing:

x + 1 ) 3x - 1 ( 3

3x + 3

-4

so (3x - 1) / (x + 1) = 3 - 4 / x+ 1

Integral of (3 - 4 / x+1 ) = 3x - 4 ln(x + 1)

Between limits of 1 and 2 we have:

(3(2) - 4 ln 3) - (3 - 4 ln2)

= 1.6056 - 0.2274

= 1.3782.

5 0

4 years ago

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line repr

BARSIC [14]

Hi there! The slope of the line is -2/5.

We can determine the slope of a line by dividing the change of y-coordinates by the change of x-coordinates.

In this situation we have a...
change of x-coordinates of (5 - 0) = 5
change of y-coordinates of (0 - 2) = -2

Therefore, the slope of this line is -2/5

6 0

4 years ago

What does PEMDAS mean in math

Dahasolnce [82]

Hey there!

PEMDAS simply means (the OVERALL question answer)

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

Here’s an example

24 - 4^2 + 2 * 4

= 24 - 16 + 2 * 4

= 24 - 16 + 8

= 8 + 8

= 16

Thus, the answer for that equation is: 16

Often people remember PEMDAS by saying. (So, I’d advise you think of it like that way as well!)

• Please
• Excuse
• My
• Dear
• Aunt
• Sally

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

8 0

3 years ago