#Differentiation- Please help no one can solve

74 messages · Page 1 of 1 (latest)

modest grail
little bluff
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To find nature of stationary point take second derivation plug the values of x from stationary points if value is negative point is maximum and if it is positive point is minimum

astral bobcat
astral bobcat
astral bobcat
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what command is it dang

modest grail
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the gradient at a stationary point is always 0 hence the name

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dont just copy chatgpt to sound smart

astral bobcat
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you can plug in to the function and compare or take the second derivative ( and look around the points ) to tell the cupping

modest grail
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what

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i tried to solve it orignally and found both poinbts to be maximiums

astral bobcat
modest grail
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yes i did that

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but there cannot be 2 maximiums

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according to google

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ok just go quiet then ig

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it seems this question is impossible because i have asked many people on multiple servers and no one knows

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even chat gpt cant do it right

astral bobcat
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I integrated the derivative

modest grail
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idk why ur using these fancy terms but if you cant do it jkust say

astral bobcat
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For this

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It's a min at 0

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clearly

modest grail
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nope

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i got
where x = 0.1
y = -0.361

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so you graph is wrong

astral bobcat
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o it's negative

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one sec

modest grail
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the graph of dy/dx = -x^3 - 4x^2 - 4x

astral bobcat
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Yeah, they are both local max

modest grail
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what

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i googled it said 2 maximiums is impossible

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wait is the origonal graph a quartix

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apparently quartics can have 2 maximiums

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maybe its right and that is why

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because if dy/dx is cubic i swear that means y=f(x) is quartic right?

astral bobcat
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if the derivative is a cubic then then function is a quartic yes

modest grail
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ok so im probably just right then?

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in the sense that i got 2 maximiums

astral bobcat
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What did you put

modest grail
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i just said they are both maximiums

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The curve y=f(x) is such that dy/dx = -x(x-2)^2 The stationary points of the curve are (0,4/3) and (2,0) Determine the nature of each point

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thats the q

woeful carbon
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jeez

woeful carbon
# astral bobcat I integrated the derivative

you dont need to integrate the derivative just find the second derivative and plug in the stationary x values to that: if it is positive its a minimum if its negative its a maximuma nd if its 0 use first derivative test

woeful carbon
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we get - 4 which means that (0,4/3) is a maximum

woeful carbon
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so f''(x) = -3x^2 + 8x - 4

woeful carbon
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so plugging in 2 to f''(x)

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we get

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0

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so we need to use first derivative test

modest grail
modest grail
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ah wait u did dy/dx on the dreivative

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i used a different method but i think both work

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eitherway ive spent to long on this ima just hand it in as hoemwork and see

woeful carbon
modest grail
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we were taught dif way

astral bobcat
eager epochBOT
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@modest grail

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astral bobcat
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— ( U2014 )

astral bobcat
woeful carbon
woeful carbon
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also i dont understand how the alt + 1234 shortcut works