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