Mathematics, 21.10.2020 16:01 irenecupcake4348

Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is continuous on − 3 2 , 12 , we can use the Closed Interval Method. f(x) = x3 − 9x2 + 3 f ′(x) = 3x2−18x . Since f ′(x) exists for all x, the only critical numbers of f occur when f ′(x) = , that is, x = 0 or x = . Notice that each of these critical numbers lies in − 3 2 , 12 . The values

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Answer from: stephanieanaya7

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).

Answer from: Quest

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180

same as (2x + 16) + (x) = 180

Answer from: Quest

answer: 35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %, p(e) = 27 % and $p(l\cap e)$ = 4 %

and, we have to find out, $p(l\cup e)$

but, we know that,

$p(l\cup e)= p(l) + p(e) - p(l\cap e)$

which is the required equation that will use to find the probability of a late departure or an early departure.

$p(l\cup e)= 12 + 27 - 4$

$p(l\cup e)= 35 %$

therefore, the probability of a late departure or an early arrival = 35 %

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

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