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
lianna [129]
3 years ago
6

Hard question but would help me out

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
4 0

Answer:

Critical value f(1)=2.

Minimum at (1,2), function is decreasing for 0 and increasing for x>1.

\left(3,\dfrac{4}{\sqrt{3}}\right) is point of inflection.

When 0<x<3, function is concave upwards and when x>3, , function is concave downwards.

Step-by-step explanation:

1. Find the domain of the function f(x):

\left\{\begin{array}{l}x\ge 0\\x\neq 0\end{array}\right.\Rightarrow x>0.

2. Find the derivative f'(x):

f'(x)=\dfrac{(x+1)'\cdot \sqrt{x}-(x+1)\cdot (\sqrt{x})'}{(\sqrt{x})^2}=\dfrac{\sqrt{x}-\frac{x+1}{2\sqrt{x}}}{x}=\dfrac{2x-x-1}{2x\sqrt{x}}=\dfrac{x-1}{2x^{\frac{3}{2}}}.

This derivative is equal to 0 at x=1 and is not defined at x=0. Since x=0 is not a point from the domain, the crititcal point is only x=1. The critical value is

f(1)=\dfrac{1+1}{\sqrt{1}}=2.

2. For 0 the derivative f'(x)<0, then the function is decreasing. For x>1, the derivative f'(x)>0, then the function is increasing. This means that point x=1 is point of minimum.

3. Find f''(x):

f''(x)=\dfrac{(x-1)'\cdot 2x^{\frac{3}{2}}-(x-1)\cdot (2x^{\frac{3}{2}})'}{(2x^{\frac{3}{2}})^2}=

=\dfrac{2x^{\frac{3}{2}}-2(x-1)\cdot \frac{3}{2}x^{\frac{1}{2}}}{4x^3}=\dfrac{2x^{\frac{3}{2}}-2\cdot\frac{3}{2}x^{\frac{3}{2}}+ 2\cdot\frac{3}{2}x^{\frac{1}{2}}}{4x^3}=

=\dfrac{-x+3}{4x^{\frac{5}{2}}}.

When f''(x)=0, x=3 and f(3)=\dfrac{3+1}{\sqrt{3}}=\dfrac{4}{\sqrt{3}}.

When 0<x<3, f''(x)>0 - function is concave upwards and when x>3, f''(x)>0 - function is concave downwards.

Point \left(3,\dfrac{4}{\sqrt{3}}\right) is point of inflection.

You might be interested in
7. Your friend is standing on top of a building, which is 130 ft. above the ground, looking down at a tree that is 40 ft. away f
oee [108]
I think you just divide the 130 ft by the 40 ft = 3.25 ??
8 0
3 years ago
A line passes through the points (4, 19) and (9, 24). Write A linear function in the form Y equals MX plus be for this line.
avanturin [10]

Answer:

y = x + 15

Step-by-step explanation:

okay so you're gonna use the y2-y1/x2-x1 formula to find the slope (m)

24 - 19/9 - 4 = 5/5 = 1

so that is your slope (m)

and now if you follow your slope then you should get your y-intercept (b)

4 - 1 = 3      19 - 1 = 18

(3, 18)

3 - 1 = 2      18 - 1 = 17

(2, 17)

2 - 1 = 1       17 - 1 = 16

(1, 16)

1 - 1 = 0       16 - 1 = 15

(0, 15)

so thats your y-intercept (b)

and the equation will look like:

y = mx + b          y = x + 15  or    y = 1x + 15 (but the 1 isn't necessary)

3 0
3 years ago
$250 at 6.5% for 3 years
Finger [1]

Answer:

hmhmhmhh hkm ntyiod dfov

Step-by-step explanation:

8 0
3 years ago
2. State two (2) values of θ (theta) to the nearest degree for<br> sin θ = − 0. 966
emmasim [6.3K]

Using equivalent angles, the solutions to the equation are given as follows:

\theta = 255^\circ, \theta = 285^\circ

<h3>What are equivalent angles?</h3>

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

\sin{\theta} = -0.966

Applying the inverse relation:

\theta = \arcsin{-0.966} = 255^\circ

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

270^\circ + (270^\circ - 255^\circ) = 285^\circ

More can be learned about equivalent angles at brainly.com/question/28025397

#SPJ1

5 0
2 years ago
Write the equation of the line in slope-intercept form using y=mx+b​
klemol [59]

Answer:

y=-2x+2

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • GUYS PLEASE HELP ME!!
    8·1 answer
  • Jim's soccer team is making fruit baskets for a fundraiser. They have 88 peaches, 60 bananas, and 54 kiwis to use. If each baske
    5·1 answer
  • What is the range of the function graphed below?
    11·2 answers
  • A birthday celebration meal is $49.20 including tax, but not the tip. Find the total cost if a 15% tip is added to the cost of t
    5·2 answers
  • Stephen averaged 32.3 points a game. LeBron averaged 29.4 points a game. What was the difference between their averages?
    15·1 answer
  • HELP!!! ASAP!!! THANK YOU !! 10 POINTS &lt;333
    7·1 answer
  • if a triangle mesures 40 degrees and 100 degrees what triangle is it Scalene Isosceles or equilateral
    13·1 answer
  • I see 2 people sitting on the bench at the playground. One was Deaf and one was blind.
    10·1 answer
  • What is John and Linda paid each hour
    14·2 answers
  • In △ABC, we are told that c=11, ∡C=75∘, and ∡B=29∘. Solve for a and b.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!