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 painter made— or quart of purple paint
Andreas93 [3]

Answer:

32 oz

Step-by-step explanation:

Im assumin you mean how many oz

3 0
2 years ago
How do I solve this problem<br>​
bija089 [108]
Attach a photo so we can see the problem
4 0
3 years ago
How many ways can you distribute $4$ identical balls among $4$ different boxes?
snow_tiger [21]

Answer:  a reasonable answer would be 4 balls maximum and 0 balls minimum to any of 4 given boxes with the 4 box totals = 4 balls.

Step-by-step explanation:

7 0
3 years ago
benny had 266 dollars to spend on 9 books. After buying them he had 14 dollars. How much did each book cost?
Anastaziya [24]

Answer:

The books cost $28 dollars each.

Step-by-step explanation:

$266 - $14 = $252

then take $252 divided by 9 = $ 28

7 0
2 years ago
What does the line y=-2x+5 look like?
Usimov [2.4K]

\huge{\boxed{\text{D}}}

This line is in the format y=mx+b, where m is the slope.

A horizontal line has a slope of 0.

A vertical line has an undefined slope.

A positive slope makes the line go upwards and to the right.

<em>A negative slope makes the line go downwards and to the right.</em>

5 0
3 years ago
Other questions:
  • In how many ways can 2 singers be selected from 4 who came for an audition?
    5·1 answer
  • Give an example of a real-world situation that could be represented by an algebraic expression
    11·1 answer
  • a regular square pyramid just fits inside a cube (the base of the pyramid is congruent to a face of the cube and the height of t
    9·1 answer
  • Pls help me with trig :)
    5·1 answer
  • Can someone help me on this problem
    6·2 answers
  • Help me with this hehe
    7·2 answers
  • Can someone pleaseeee help if you’re correct I’ll give u brainlist
    10·1 answer
  • Elen inwests $100.000 in an account paying 75% interest compounded continuously , How much
    9·1 answer
  • State the correct answers.​
    9·2 answers
  • Members of a softball team raised $1405.25 to go to a tournament. They rented a bus for $822.50 and budgeted $27.75 per player f
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!