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3 years ago

Need help plzzzzzzzzzzz

Mathematics

2 answers:

Sauron [17]3 years ago

6 0

Answer: the answer should be 16

Step-by-step explanation:

Elena-2011 [213]3 years ago

4 0

The answer is 16. I’ve done this before and i got a 100% on it! Good Luck!!

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Consider the following function. f(x) = 2x3 + 9x2 − 24x (a) Find the critical numbers of f. (Enter your answers as a comma-separ

viktelen [127]

Answer:

(a) The critical number of $f(x)$ are $x=-4, 1$

(b)

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c)

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

Step-by-step explanation:

(a) The critical numbers of a function are given by finding the roots of the first derivative of the function or the values where the first derivative does not exist. Since the function is a polynomial, its domain and the domain of its derivatives is $(-\infty, \infty)$ . Thus:

$\frac{df(x)}{dx} = \frac{d(2x^3+9x^2-24x)}{dx} =6 x^2+18x -24\\6 x^2+18x -24=0\\\boxed{x=-4, x=1}$

(b)

A function $f(x)$ defined on an interval is monotone increasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)$

A function $f(x)$ defined on an interval is monotone decreasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)>f(x_2)$

Combining the domain $(-\infty, \infty)$ with the critical numbers we have the intervals $(-\infty, -4)$ , $(-4, 1)$ and $(1, \infty)$ . Note that any of the points are included, in the case of the infinity it is by definition and the critical number are never included because the function monotony is not defined in the critical points, i.e. it is not monotone increasing or decreasing. Now, let's check for the monotony in each interval, for this, we check for the sign of the first derivative in each interval. Evaluating in each interval the first derivative (one point is enough), we obtain the monotony of the function to be:

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c) From the values obtained in (a) so the relative extremum are the points $(-4, 112)$ and $(1, -13)$ . The $y$ -values are found by evaluating the critical numbers in the original function. Since the first derivative decreases after passing through $x=-4$ and increases after passing through the point $x=1$ we have:

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

3 0

4 years ago

Can you please help me with this question

cestrela7 [59]

8,9 2,4 1,8 hope this may help!!

8 0

3 years ago

Read 2 more answers

I need help with the following question, whichever one is right will get brainliest!

Schach [20]

Given: m∠A + m∠B = 90° (Definition of Complementary Angles).

Given: m∠B = (5x + 8)°

A) m∠A = 180° + (5x + 8) is your answer choice:

Why it isn't the others:

B) m∠A = 90° - (5x + 8)

You are solving for complementary angles (90° in total when combined), so you subtract the measurement for B (5x + 8) to get A.

C) m∠A = 180° - 2(5x + 8)°

You double the complementary angle to solve for the supplementary. Essentially, just divide this answer by two to get the complementary angles.

D) m∠A = 82 - 5x

I was confused by this one, but essentially they just did one step of the isolating the variable, which was subtracting 8 from both sides. They did not finish isolating the variable however.

8 0

3 years ago

Two people are standing on opposite sides of a hill. Person A makes an angle of elevation of 65° with the top of the hill and pe

Artyom0805 [142]

The rest of the question is as following
What is the distance from person B to the top of the hill?
===================================================
Answer;
The attached figure represents the explanation of the problem.
So, it is required to find the distance BH
It will be calculated as following
∠A = 65° and ∠B = 80°
∴ ∠H = 180° - (65° + 80° ) = 35°
But the side AB = 45
So, we can use the sine rule to find the side BH
$\frac{AB}{sin \ H} = \frac{BH}{sin \ A}$
$BH = \frac{sin \ A}{sin \ H} * AB$
$BH = \frac{sin \ 65}{sin \ 35} * 45$

∴ BH ≈ 71.1 feet

∴ The distance from person B to the top of the hill ≈ 71.1 feet

7 0

3 years ago

Read 2 more answers

Larry wants to start an IRA that will have $810,000 in it when he retires in 19 years. How much should he invest semiannually in

MissTica

The way I calculated it shows the answe would be a

6 0

3 years ago