#Can anyone answer this

104 messages · Page 1 of 1 (latest)

peak sundialBOT
amber barn
upper current
#

g(x) is the first derivative of f(x)

#

so for a maximum g(x) = 0 aka roots
and g'(x) has a change of sign before and after root from + to -

amber barn
#

sofor what value f(x) is max??

upper current
#

Think

#

Oh I also just realized they are showing f(x) in the figure not g(x) so it's even easier

amber barn
#

is that d

upper current
#

explain yourself

amber barn
upper current
#

What is this supposed to be?

amber barn
#

its graph of g(t)

upper current
#

How

#

The task says "The graph of f(x)"

amber barn
#

yesss

#

i seee that now

upper current
#

It's weird though

#

I have a feeling they made a typo

#

It would make more sense if the graph was g(t)

amber barn
#

maybe

upper current
#

But assuming it's f(x) what would be here the max it's obvious

amber barn
#

and if it is graph of g(t) d is max

upper current
#

no stop

#

first answer my question

upper current
amber barn
upper current
#

Ok good

#

Now if it were g(t)?

amber barn
#

d

upper current
upper current
amber barn
#

still b??

upper current
#

the second condition is change of sign

#
  • -> - for maximum
#

At which root does that happen

#

Where is g(t) > 0 and then g(t) < 0

#

Where does that happen

#

You got 3 roots

#

d is wrong

#

You cant say how the function proceeds further

#

@amber barn

amber barn
#

i am confused @upper current

upper current
#

No

#

you never heard of the second condition change of sign?

amber barn
#

no

#

i am a beginner

upper current
#

before a maximum the first derivative is positive and after it's negative

#

,w plot -x^2

quaint sphinxBOT
upper current
#

Here example

#

max is at x = 0

#

tangent line slope 0

#

before that

#

the slope was positive and after it is negative

#

so between the root of the first derivative there was a change of sign from + to -

upper current
#

g(t) describes the slope of f(x)

#

at which root is g(t) > 0 before and after g(t) < 0

#

You only got 3 options

#

3 roots

#

d is wrong

#

what about a?

amber barn
#

lemme think

upper current
#

ok

amber barn
#

ok i understood that

upper current
#

continue then what should be the answer

amber barn
#

a

upper current
#

looks like you didnt understand

#

how can you tell how g(t) behaves before a

#

you cant

#

so c is remaining really

#

now tell me

#

before c if g(t) is postive or negative and the same after c

amber barn
#

omg i understood now , as the curve from c to d is below x-axis

#

g(t) is negative , and before c g(t) is positive , am I getting that right @upper current

upper current
#

Yes

#

Thats exactly

amber barn
#

Okay so our final answer is c if the graph if of g(t)

upper current
#

Yes

#

,w plot sinx and cosx between 0 and pi

quaint sphinxBOT
upper current
#

Here cosine is the first derivative of sine

#

And you see the exact same phenomenon

#

root at x = π/2 and change of sign from + to -

#

hence maximum

amber barn
#

yes

upper current
#

For a minimum it's the opposite

#

You look for - to + change of sign

#

,w plot -sinx and -cosx between 0 and pi

quaint sphinxBOT
upper current
#

now minimum and the yellow function the cosine goes from - to +

amber barn
#

here function is minimum at pi/2

upper current
#

Yes

amber barn
#

i got that

upper current
#

Thats literally it

#

necessary condition is always first derivative equal 0

#

If there are solutions

look for change of sign as that is the sufficient condition

#
  • to - is max

- to + is min

amber barn
#

okay

#

thanks for helping me @upper current

upper current
#

thanks for understanding @amber barn

peak sundialBOT
#

If you are done with this channel, please mark your problem as solved by typing .close

amber barn
#

.close