MATHEMATICS COLLEGE

Find the critical points, domain endpoints, and local extreme values for the functiony=x^2/5(x+3)

a. What is/are the critical point(s) and domain endpoint(s) where f' is undefined?
b. What is/are the critical point(s) and domain endpoint(s) where f' is 0?
c. From the critical point(s) and domain endpoint(s), what is/are the points corresponding to local maxima?
d. From the critical point(s) and domain endpoint(s), what is/are the points corresponding to local minima?

Answers

Answer 1

Answer:

Answer:

a) $x = -3$ , b) $x = 0$ , $x = -6$ , c) $x = 0$ , d) $x = -6$

Step-by-step explanation:

a) Let derive the function:

$f'(x) = (10\cdot x \cdot (x+3)-5\cdot x^(2))/(25\cdot (x+3)^(2))$

$f'(x)$ is undefined when denominator equates to zero. The critical point is:

$x = -3$

b) $f'(x) = 0$ when numerator equates to zero. That is:

$10\cdot x \cdot (x+3) - 5\cdot x^(2) = 0$

$10\cdot x^(2)+30\cdot x -5\cdot x^(2) = 0$

$5\cdot x^(2) + 30\cdot x = 0$

$5\cdot x \cdot (x+6) = 0$

This equation shows two critical points:

$x = 0$ , $x = -6$

c) The critical points found in point b) and the existence of a discontinuity in point a) lead to the conclusion of the existence local minima and maxima. By plotting the function, it is evident that $x = 0$ corresponds to a local maximum. (See Attachment)

d) By plotting the function, it is evident that $x = -6$ corresponds to a local minimum. (See Attachment)

Related Questions

Pls help meeeeeeeeeeeeeeeeeeeeeeeee
2. Half of the pieces of fruit in the bowl are apples. There arealso 3 oranges, 2 pears, and a banana. How many apples are there in the bowl? Show your work!
there are 8 tennis balls in a bag.five of the balls are yellow and the other 3 are green, what's the probability of pulling out a green ball without looking? write your answer as a decimal
Factor out the GCF of (2x+1)
lled a 12:3:112:3:1 ratio. Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2:131F2:131 white squash, 3434 yellow squash, and 1010 green squash. Are these data consistent with a 12:3:112:3:1 dominant epistatic model of genetic inheritance( white being dominant)? The null hypothesis for the chi‑square goodness‑of‑fit test is

Assuming the weights are in kilograms, what is the mystery weight of y Use the equation you created in part A to find thesolution
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for a fraction bar

Answers

The Answer To Your Question is 1/2

Answer:

y = 1/2 kilogram(s)

Step-by-step explanation:

Solve the equation created from the model for y:

A customer has $10 to spend at the concession stand. Hotdogs cost $2 each and drinks cost $2.50 each. Graph the inequality that illustrates this situation. Use the space below to explain what the answer means.

Answers

Answer:

Please refer to the graph in the attached area.

Step-by-step explanation:

Given:

Total money available with the customer is $10.

Cost of each hotdog is $2.

Cost of each drink is is $2.50.

To find:

The graph of inequality.

Solution:

Let number of hotdogs bought = $x$

Total cost of hotdogs = $2x$

Let number of drinks bought = $y$

Total cost of drinks = $2.5y$

Total cost = $2x+2.5y$

And total money available is $10.

So, the total cost calculated above must be lesser than or equal to $10.

Hence, the inequality is:

$2x+2.5y<10$

Also there will be two conditions on variables $x$ and $y$ :

$x\ge0\ny\ge0$

To graph this, let us find the points on the equivalent equation:

$2x+2.5y = 10$

Finding two points on the equation.

First put x = 0 $\Rightarrow$ y = 4

Then put y = 0, $\Rightarrow$ x = 5

So, two points are (0, 4) and (5, 0).

Now, plotting the line.

Having point (1,2) in the inequality:

2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)

Please refer to the graph of inequality in the attached graph.

I NEED HELP ASAP PLEASE HELP

Answers

Answer: C

Step-by-step explanation:

Answer:

Answer: C

Step-by-step explanation:

When looking at the whole number, You always want to look at the tenths place to see of it's 5 or higher.

Ms.Johnson walks at a rate of 2 miles per hour so many miles does she walk in 1 hour?

Answers

Answer:

2 miles

Step-by-step explanation:

We know

Ms. Johnson walks at a rate of 2 miles per hour.

How many miles does she walk in 1 hour?

2 miles

Valerie wants to take out a discount loan of $569. The rate is 4.5% for 250 days. How much interest will she pay? (Be sure to round the time to the nearest hundredth.

Answers

The interest is computed from

... I = Prt

where P is the principal amount ($569), r is the rate (0.045) and t is the time in years (250/360).

... I = $569×0.045×250/360 ≈ $17.78

Please note that time is not rounded. Rather, the exact value (25/36) is used in the calculation. The only rounding of any number is done at the end, where the amount is rounded to the nearest cent. (Your text authors should know this.)

_____

If you follow the problem instructions (which Valerie's lender will not do), the interest is calculated as ...

... t = 250/360 = 0.6944444... ≈ 0.69 . . . . years

... I = $569×0.045×0.69 ≈ $17.67

_____

Note the rounding of intermediate numbers (time) introduces an error of about $0.11 in the answer.

Answer:$17.41 (A+)

Step-by-step explanation:

30 POINTS! PLEASE GRAPH AND ANSWER THE QUESTION WILL MARK BRANLIEST

Answers

Answer:

Step-by-step explanation:

put a point on -5 and put a point on -4 then write the equation on the top to show what you did, name the points then put a point on -9

Answer:

x ≥ 1

Step-by-step explanation:

Move all terms not containing x to the right side of the inequality.

−x ≤ −1

Divide each term in −x ≤ −1 by −1 and simplify.

x ≥ 1

Hope this helps! :)

Other Questions

What is the solution of the following quadratic inequality? x2 – 4x – 21 ≤ 0

Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f (x )equals8 x minus 5 (A) [0,4] (B) [negative 4 comma 3 ]

1) Between which two integers does the square root of 48 lie? *

A point travels East 3 spaces and South 8 spaces.Write the description in algebraic terms.