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
Bond [772]
3 years ago
11

Need help and explain please!!

Mathematics
1 answer:
lukranit [14]3 years ago
3 0

Answer:

x=-4\text{ and } x=3

Step-by-step explanation:

We are given the second derivative:

g''(x)=(x-3)^2(x+4)(x-6)

And we want to find its inflection points.

To do so, we will first determine possible inflection points. These occur whenever g''(x) = 0 or is undefined.

Next, we will test values for the intervals. Inflection points occur if and only if the sign changes before and after the point.

So first, finding the zeros, we see that:

0=(x-3)^2(x+4)(x-6)\Rightarrow x=-4, 3, 6

So, we can draw the following number-line:

<----(-4)--------------(3)----(6)---->

Now, we will test values for the intervals x < -4, -4 < x < 3, 3 < x < 6, and x > 6.

Testing for x < -4, we can use -5. So:

g^\prime^\prime(-5)=(-5-3)^2(-5+4)(-5-6)=704>0

Since we acquired a positive result, g(x) is concave up for x < -4.

For -4 < x < 3, we can use 0. So:

g^\prime^\prime(0)=(0-3)^2(0+4)(0-6)=-216

Since we acquired a negative result, g(x) is concave down for -4 < x < 3.

And since the sign changed before and after the possible inflection point at x = -4, x = -4 is indeed an inflection point.

For 3 < x < 6, we can use 4. So:

g^\prime^\prime(4)=(4-3)^2(4+4)(4-6)=-16

Since we acquired a negative result, g(x) is concave down for 3 < x < 6.

Since the sign didn't change before and after the possible inflection point at x = 3 (it stayed negative both times), x = -3 is not a inflection point.

And finally, for x > 6, we can use 7. So:

g^\prime^\prime(7)=(7-3)^2(7+4)(7-6)=176>0

So, g(x) is concave up for x > 6.

And since we changed signs before and after the inflection point at x = 6, x = 6 is indeed an inflection point.

You might be interested in
The sum of two numbers is nine. If one number is subtracted from the other, the result is -3. Find the numbers
12345 [234]

Answer:

3,6

Step-by-step explanation:

x+y=9

x-y=-3

Adding these two equations we get 2x = 6, x=3

y=6

3 0
3 years ago
Find x helpppppppppppp​
lidiya [134]

|2x - 1|  =  | - x - 2|

Thus ;

2x - 1 =  - x - 2

Add both sides x

2x + x - 1 =  - x + x - 2

3x - 1 =  - 2

Add both sides 1

3x - 1 + 1 =  - 2 + 1

3x =   - 1

Divide both sides by 3

\frac{3x}{3}  =  \frac{ - 1}{3}  \\

x =  -  \frac{1}{3}  \\

<h2>Or </h2>

2x - 1 =  - ( - x - 2)

2x - 1 = x + 2

Subtract both sides x

2x  - x  - 1 = x - x + 2

x - 1 = 2

Add both sides 1

x - 1 + 1 = 2 + 1

x = 3

There u go ...

3 0
2 years ago
PLEASE ANSWER FAST<br> what is the length of rt?<br> a - 3 cm <br> b - 1 cm<br> c- 9 cm<br> d - 4 cm
defon

Answer:

I would say 3cm

Step-by-step explanation:

sorry if it's wrong but I sure it's right

4 0
2 years ago
Read 2 more answers
Do you think this Scatter plot is linear or no? I really can't tell.
MrRa [10]

Answer:

I would say no because the dots are all over the place.

Step-by-step explanation:

It keeps going up then down back up and down again?

4 0
3 years ago
HELPP ASAPP!!!!!!!!!!!!!!!!
kati45 [8]

Answer:

y = 18

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • given the equation y=-2x^2+1. determine the direction of opening, coordinates of the vertex, Maximum or minimum value and the ax
    10·1 answer
  • On friday 1/6 of band pracitce was spent trying on uniforms. the band spent 1/6 of practice on marching, the remaining practice
    10·1 answer
  • 7.5% of the box office receipts on a Friday night are $270. What are is the total length box office receipts
    10·1 answer
  • You are skiing down a mountain with a vertical height of 1800 feet. the distance from the top of the mountain to the base is 360
    13·1 answer
  • What is f(x) = 8x^2 + 4x written in vertex form?
    8·1 answer
  • You have 7 books,but only 3 will fit on the shelf.how many different arrangements of 3 books out of 7 could you make
    14·1 answer
  • How to find the scale factor of triangles
    7·1 answer
  • What is 3/14 divided by 7/10
    7·2 answers
  • the volume of a large aquarium is 210 ft. it is 5 ft wide and 6 ft high. what is the length of the aquarium?
    15·2 answers
  • 24÷2[70÷5{4+(12-(12-8÷6×3)}]​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!