1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elena L [17]
3 years ago
10

Find the critical points, domain endpoints, and local extreme values for the function

Mathematics
1 answer:
aliina [53]3 years ago
8 0

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) = \frac{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)

You might be interested in
Irene is going to read a 216-page book.
shepuryov [24]

Answer:

4 days

Step-by-step explanation:

216/3 = 72

72/18 = 4

8 0
3 years ago
PLEASE HELP WITH THIS
tankabanditka [31]

Answer:

Step-by-step explanation:

i Don't now how to explain the answer

8 0
3 years ago
PLEASE HELP ME!!<br> (Geometry)
telo118 [61]

Answer:

a = -7

B= *4

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Help me with the last part at the bottom please it says x =
lukranit [14]

Answer:

Step-by-step explanation:

x = 0.8 + 0.2y

7 0
3 years ago
Choose the fraction that has not been reduced 10-19, 15-16,19-38,21-34
BartSMP [9]
19/38 is not reduces. Numerator and denominator can be divided by 19.
It can be reduced to 1/2
4 0
3 years ago
Other questions:
  • Easy + brainliest<br><br> 2x(^3) + 10x(^2) − 4x(^2)y − 20xy<br><br> factor this pls, (show all work)
    5·2 answers
  • Joel earns 1,700 per month if he spends $425 on rent each month what percent of his income does he spend on rent
    14·1 answer
  • What is (x)=8.00+0.20x
    13·2 answers
  • Please help, I can't figure out where to plot my points.
    13·1 answer
  • A die is rolled twice. what is the probability of showing a 3 on both rolls?
    12·1 answer
  • Okay, I tried this a bunch of times but never found out. <br> Simplify the expression:<br> 4(b-6)+19
    14·1 answer
  • Blue cassettes hold 45 minutes of music. Green cassettes hold 55 minutes
    8·1 answer
  • What is the total surface area?
    15·2 answers
  • a group buys 6 hot dogs and 3 hamburgers for a total of $27.75. the hamburgers cost $1.75 more than a hot dog. what is he cost o
    8·1 answer
  • Rewrite 72.3 + (-39.1) by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!