Fall 2019

Total marks: 10

Due Date: 30th December, 2019

DON’T MISS THESE: Important instructions before attempting the solution of this assignment:

• To solve this assignment, you should have good command over 16-22 lectures.

• Try to get the concepts, consolidate your concepts which you learn in these lectures with these questions.

• Upload assignments properly through LMS, No Assignment will be accepted through email.

• Write your ID on the top of your solution file.

• Don’t use colorful back grounds in your solution files.

• Use Math Type or Equation Editor etc for mathematical symbols.

• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.

• Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.

• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.

Question:

If Find the intervals where the given function is

- Increasing
- Decreasing
- Concave up
- Concave down respectively.

Also find the point of inflection for the given function.

Fall 2019

Total marks: 10

Due Date: 30th December, 2019

DON’T MISS THESE: Important instructions before attempting the solution of this assignment:

• To solve this assignment, you should have good command over 16-22 lectures.

• Try to get the concepts, consolidate your concepts which you learn in these lectures with these questions.

• Upload assignments properly through LMS, No Assignment will be accepted through email.

• Write your ID on the top of your solution file.

• Don’t use colorful back grounds in your solution files.

• Use Math Type or Equation Editor etc for mathematical symbols.

• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.

• Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.

• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.

Question:

If Find the intervals where the given function is

- Increasing
- Decreasing
- Concave up
- Concave down respectively.

Also find the point of inflection for the given function.

Solution:

```
Increasing
```

f(x)=x3-27x

After Taking Derivative

f `(x)=3x2-27

Function will increase if it is greater than zero

f `(x)=3x2-27>0

3x2-27>0

x2-9>0

x2>9

After taking square root

x>3

So, function increase on (3,∞)

```
Decreasing
```

f(x)=x3-27x

Take Derivative

f `(x)=3x2-27

Function will decrease when it is less than zero

f `(x)=3x2-27<0

3x2-27<0

x2-9<0

x2<9

After taking square root

x<3

So, function decrease on (- ∞, 3)

```
Concave up
```

f(x)=x3-27x

After Taking Derivative

f `(x)=3x2-27

After taking second derivative

f ``(x)=6x

f ``(x)=6x>0

6x>0

x>0

So, it is concave up on (0,+∞)

```
Concave down
```

f(x)=x3-27x

After Taking Derivative

f `(x)=3x2-27

After taking second derivative

f ``(x)=6x

f ``(x)=6x<0

6x<0

x<0

So, it is concave down on (- ∞,0)

POINT OF INFLECTION

f(x)=x3-27x ------------------ (1)

After Taking Derivative

f `(x)=3x2-27

After taking second derivative

f ``(x)=6x

f ``(x)= 6x =0

6x=0

x=0

Put this in (1)

f(0)=(0)3- 27(0)

f(0)=0

So, inflection point is (0 , 0)

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