Math, asked by maheshwarkrithik, 4 days ago

8) Find the maximum or minimum values of f(x,y) = 3x^2-y^2+x^3​

Answers

Answered by grsharma31
0

Step-by-step explanation:

sᴇᴀʀᴄʜ-ɪᴄᴏɴ-ʜᴇᴀᴅᴇʀ

sᴇᴀʀᴄʜ ғᴏʀ ǫᴜᴇsᴛɪᴏɴs & ᴄʜᴀᴘᴛᴇʀs

sᴇᴀʀᴄʜ-ɪᴄᴏɴ-ɪᴍᴀɢᴇ

ᴄʟᴀss

>>ᴍᴀᴛʜs

>>ғᴀᴄᴛᴏʀɪsᴀᴛɪᴏɴ

>>ғᴀᴄᴛᴏʀɪsᴀᴛɪᴏɴ

>>x^ - x - . | ᴍᴀᴛʜs ǫᴜᴇsᴛɪᴏɴs

ǫᴜᴇsᴛɪᴏɴ

ʙᴏᴏᴋᴍᴀʀᴋ

x

−x−.

ʜᴀʀᴅ

sᴏʟᴜᴛɪᴏɴ

ᴠᴇʀɪғɪᴇᴅ

ᴠᴇʀɪғɪᴇᴅ ʙʏ ᴛᴏᴘᴘʀ

ɪɴ ᴛʜᴇ ɢɪᴠᴇɴ ᴘᴏʟʏɴᴏᴍɪᴀʟ x

−x−,

ᴛʜᴇ ғɪʀsᴛ ᴛᴇʀᴍ ɪs x

ᴀɴᴅ ɪᴛs ᴄᴏᴇғғɪᴄɪᴇɴᴛ ɪs .

ᴛʜᴇ ᴍɪᴅᴅʟᴇ ᴛᴇʀᴍ ɪs −x ᴀɴᴅ ɪᴛs ᴄᴏᴇғғɪᴄɪᴇɴᴛ ɪs −.

ᴛʜᴇ ʟᴀsᴛ ᴛᴇʀᴍ ɪs ᴀ ᴄᴏɴsᴛᴀɴᴛ ᴛᴇʀᴍ −.

ᴍᴜʟᴛɪᴘʟʏ ᴛʜᴇ ᴄᴏᴇғғɪᴄɪᴇɴᴛ ᴏғ ᴛʜᴇ ғɪʀsᴛ ᴛᴇʀᴍ ʙʏ ᴛʜᴇ ᴄᴏɴsᴛᴀɴᴛ ×−=−.

ᴡᴇ ɴᴏᴡ ғɪɴᴅ ᴛʜᴇ ғᴀᴄᴛᴏʀ ᴏғ − ᴡʜᴏsᴇ sᴜᴍ ᴇǫᴜᴀʟs ᴛʜᴇ ᴄᴏᴇғғɪᴄɪᴇɴᴛ ᴏғ ᴛʜᴇ ᴍɪᴅᴅʟᴇ ᴛᴇʀᴍ, ᴡʜɪᴄʜ ɪs − ᴀɴᴅ ᴛʜᴇɴ ғᴀᴄᴛᴏʀɪᴢᴇ ᴛʜᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ x

−x− ᴀs sʜᴏᴡɴ ʙᴇʟᴏᴡ:

x

−x−

=x

+x−x−

=x(x+)−(x+)

=(x−)(x+)

ʜᴇɴᴄᴇ, x

−x−=(x−)(x+).

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