What the answer to this

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

This is a 3 question thing! HELP!

romanna [79]

Answer:

Step-by-step explanation:

MR=2x-1. First equation

RP=9x+3 second equation

MP=MR+RP third equation

MP= 2x-1+9x+3 first equation plus second equation

MP=11x+2

MP=57

57=11x+2 replaced MP value

57-2=11x

55=11x

55/11=x

X=5

6 0

4 years ago

Which of the following is a property of all rectangles?

Sliva [168]

Answer:

All angles are right angles. The diagonals are congruent. And it's a parallelogram

Step-by-step explanation:

6 0

3 years ago

12. On a math test, Ana writes 9 as the solution to 27.<br> PART A<br> Find the correct solution.

scoray [572]

Answer:

11. B.

12. 3

Step-by-step explanation:

$\sqrt{81}-\sqrt{25}=9-5=4$

$\sqrt[3]{27}=3$ since $3^{3}$ $=27$

4 0

3 years ago

Read 2 more answers

State the horizontal asymptote of the rational function. f(x) = quantity x squared plus three x minus two divided by quantity x

omeli [17]

$f(x)=\dfrac{x^2+3x-2}{x-2}\\ D_f=\mathbb{R}\setminus\{2\}\\\\ \displaystyle \lim_{x\to \infty}\dfrac{x^2+3x-2}{x-2}=\lim_{x\to \infty}\dfrac{x\left(x+3-\dfrac{2}{x}\right)}{x\left(1-\dfrac{2}{x}\right)}=\lim_{x\to \infty}\dfrac{x+3-\dfrac{2}{x}}{1-\dfrac{2}{x}}=\dfrac{\infty}{1}=\infty\\ \lim_{x\to -\infty}\dfrac{x^2+3x-2}{x-2}=\lim_{x\to -\infty}\dfrac{x\left(x+3-\dfrac{2}{x}\right)}{x\left(1-\dfrac{2}{x}\right)}=\lim_{x\to -\infty}\dfrac{x+3-\dfrac{2}{x}}{1-\dfrac{2}{x}}=\dfrac{-\infty}{1}=-\infty$

The limits are not numbers, so the asymptote doesn't exist.

8 0

3 years ago