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
What inequality is represented by this graph? 12 2 3 0128 o a 128​
steposvetlana [31]

Answer:

Please edit this question, I'm not sure what you're asking. Or, include a picture.

3 0
3 years ago
X2 – 5x + 6 = 0 solve.
Strike441 [17]
When you factor you get (x-2)(x-3)=0 then x=2 and x=3
4 0
3 years ago
Simplify the following expression and justify each step in your simplification. 5(7-x)+6x(3x+4)
Mariulka [41]
35-5x+18x^2+24x 
Simplify:
18x^2+19x+35
8 0
3 years ago
Read 2 more answers
I'll give BRAINIEST<br><br> .............
Andrew [12]
Its 0.25. ez. i hope i helped :)

3 0
3 years ago
A carpet layer can put down 400 square feet of carpet in 2.5 hours. How many hours will it take to lay down 600 square feet of c
Tresset [83]
First take 400 and divide it by 2.5 to find the hourly rate. Then divide 600 by the hourly rate (160) to get 3.75 hours. My work is listed below.

5 0
3 years ago
Other questions:
  • What is the solution of this equation? 1/3y = -7
    8·1 answer
  • Write the equation of the function g(x) if g(x) = f(x+2) +4 and f(x) = x^3 -7
    6·1 answer
  • A bookworm burrows a hole through an eight-volume set of encyclopedia from the start of Volume 4 right through to the end of Vol
    8·1 answer
  • PLEASE HELP!!!!!!!! FIRST TO ANSWER WILL GET BRAINLIEST!!!
    13·1 answer
  • Can you help me with this problem <br> 7y-2(8y+1)=4
    5·1 answer
  • 30 min before test please help !!numbers 13 and 14
    8·1 answer
  • What is the answer to this equation 39/25 × 10/99 × 27/26=
    15·1 answer
  • HELP ME PLEASE!!!
    8·1 answer
  • Jake is 2 years younger than Alex. Alex is 1 year older than James. James is twice the age of Amy. When you add all their ages,
    9·2 answers
  • Can someone help me with my geometry
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!