Without calculating the product is 5 x 6/5 greater or less than 5 and why?

A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum val

Taya2010 [7]

Answer:

The local maximum and minimum values are:

Local maximum

$g(0) = 0$

Local minima

$g(5.118) = -350.90$

$g(-1.368) = -9.90$

Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

$g(x) = x^{2}\cdot (x^{2}-5\cdot x -14)$

Then, first and second derivatives of the function are, respectively:

First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

$g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}$

$g'(x) = 4\cdot x^{3}-15\cdot x^{2}-28\cdot x$

$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:

$x\cdot (x-5.118)\cdot (x+1.368) = 0$

The critical points are 0, 5.118 and -1.368.

Each critical point is evaluated at the second derivative expression:

x = 0

$g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28$

$g''(0) = -28$

This value leads to a local maximum.

x = 5.118

$g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28$

$g''(5.118) = 132.787$

This value leads to a local minimum.

x = -1.368

$g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28$

$g''(-1.368) = 35.497$

This value leads to a local minimum.

Therefore, the local maximum and minimum values are:

Local maximum

$g(0) = (0)^{4}-5\cdot (0)^{3}-14\cdot (0)^{2}$

$g(0) = 0$

Local minima

$g(5.118) = (5.118)^{4}-5\cdot (5.118)^{3}-14\cdot (5.118)^{2}$

$g(5.118) = -350.90$

$g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}$

$g(-1.368) = -9.90$

7 0

3 years ago

What is an equivalent expression to 3^5?

Roman55 [17]

Answer:

3^5= 3 times 3 times 3 times 3 times 3 or 243

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Stuck on this question... will give brainliest

Sveta_85 [38]

Answer:

which qn..?

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Which statement(s) about the graph are correct? Select ALL that apply.

hoa [83]

Answer: B and D are correct.

Step-by-step explanation:

A is wrong because they will eventually intersect (the arrows show that the line continues on).

B is correct; that is where they will intersect.

C is wrong because they only intersect at one point, and that's where the solution is.

D is correct because they intersect once and have only one solution.

3 0

3 years ago

After graduation your first job is with abibas inc., a company that specializes in sportswear with collegiate logos. to improve

Aleksandr [31]

The probability that the new UNC-CH logo will be profitable is <u>0.9897 </u>while the probability for NC State will be <u>0.9600.</u>

<h3 /><h3>What is the probability that the brands will be successful?</h3>

The probability that the UNC-CH logo is successful is:

= Favorable odds / Total odds

= 96 / (96 + 1)

= 0.9897

The probability that the NC State logo is profitable is:

= Favorable odds / Total odds

= 24 / (24 + 1)

= 0.9600

There is less than a 3% variation in both logos' profitablility probability so the company should not spend 4 times more on UNC-CH.

Find out more on probabilities of profit at brainly.com/question/13500115.

#SPJ1

4 0

2 years ago