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]
2 years ago
11

Need help and explain please!!

Mathematics
1 answer:
lukranit [14]2 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
What is 2.24 rounded to the nearest tenth?
quester [9]
One tenth is 0.1.  Therefore, the answer has to be 2.x.  Since 4 is less than 5, the 2 remains the same.  The answer is 2.2.  
3 0
2 years ago
Read 2 more answers
Which expression is equivalent to (5m) ^3
Evgen [1.6K]

Answer:

5mx5mx5m

Step-by-step explanation:

Mulyiply 5m three timea

3 0
3 years ago
Read 2 more answers
What is the means-to-MAD ratio of the two data sets, expressed as a decimal?
Ksenya-84 [330]
I think the answer is 1.2
7 0
2 years ago
(i will give brainliest for the first answer)
labwork [276]

Answer:  X"  ( -3,2)    Y" (-1,0)   Z" (1,6)

Step-by-step explanation:

3 0
2 years ago
Sam spent $16 on a large pizza and two drinks. If the pizza was 75% of the cost, how much did each drink cost?
Veseljchak [2.6K]

Each drink costs $2.

7 0
2 years ago
Other questions:
  • The histogram shows the weekly rates charged by different daycares for a 2-year-old child.
    6·1 answer
  • Original price $29.99, markdown is 33 1/3%
    12·1 answer
  • A sealed rectangular box measuring 8•6•18 contains 864 sugar cubes, each measuring 1•1•1. How many sugar cubes are touching the
    10·2 answers
  • 15 points!!! GEOMETRY help please!!<br> Questions attached!
    11·1 answer
  • For a linear model with a dependent variable Y and two independent variables X1 and X2, write out[1] the objective functions to
    8·1 answer
  • How much will a cube shaped box hold if each side measures 3.5ft
    9·1 answer
  • Simplify 4√27 + 6√75
    15·2 answers
  • Does the frequency distribution appear to have a normal​ distribution? Explain. Temperature ​(degrees​F) Frequency 35 dash 39 1
    13·1 answer
  • Math unit rate can someone please help me
    7·1 answer
  • Pls help plssssss thank you 20 points
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!