Question

Checking my answers
if f(x)=x^3-9x^2+15x+3

What is the relative maxima ?

Answer 1

I got 10.

Answer 2

Really??

Answer 3

Yeah really.

Answer 4

It will be right as it is calculated by the Great @hba

ha ha ha..

Answer 5

Thanks.

Answer 6

I have more question to get checked can i ask here or in a new post.

Answer 7

I don't know how to solve these types of questions..

Can you teach me how to solve it..??

Answer 8

@waterineyes

Ha Ha Ha Nice joke,first let me ask my questions.

Answer 9

First, we will take derivative..

Right??

Answer 10

Yeah.

Answer 11

So wait, I am doing it..

Answer 12

okay :(

Answer 13

f'(x) = 3x^2 - 18x + 15

Answer 14

there are two extrema, 1 relative maximum and 1 relative minimum.

Answer 15

Should I factorize it??

Answer 16

put f'(x)=0

Answer 17

Yes I mean the same..

Answer 18

Then the answer is yes

Answer 19

\[x^2 - 6x + 5 = 0 \implies (x - 5)(x - 1) = 0\]

Answer 20

x = 5 and x = 1

Answer 21

Yes you are right

Answer 22

Now put 1 in the orignal equation.

Answer 23

Why not 5 ??

Answer 24

Because we are finding the relative maxima

Answer 25

f(1) = 10

Answer 26

oooh, i misread the problem. relative maxima.

Answer 27

Correct.

Answer 28

So, we have to put smaller value??

Answer 29

Yes.

Answer 30

Just checking your answer..

Ha ha ha..

Answer 31

Now don't say, to find relative minima, we will put 5..

Answer 32

@waterineyes Check these two questions.

Answer 33

How to solve these now??

Answer 34

I got f'(x)=e in both the cases.

Answer 35

And f''(x)=1/e

for 1st

and

f''(x)=e

in the 2nd one.

Answer 36

So i am right ?

Answer 37

Are you sure it is e ??

Answer 38

Pretty sure

Because i did this one like 100 times when i was in High school

Answer 39

You have used division rule here??

Answer 40

U/V form.

Answer 41

For first :

\[f'(x) = \frac{1 - \ln(x)}{x^2}\]

Answer 42

Wait lemme check.

Answer 43

Take your time..

Answer 44

Yeah right

Answer 45

@waterineyes ?

Answer 46

Who is right??

Answer 47

The most intelligent @waterineyes

Answer 48

Not intelligent as you @hba

Answer 49

Now, find the second derivative..

Answer 50

Ha Ha Ha

Yeah wait.

Answer 51

I am getting something,which looks extremly wrong :/