Find the equation of tangent

why should 3a^2=(b-2)/a

Let the touching point (a

b) dy/dx = 3x^2 At (a

b)

the slope of tangent line that pass through the point (0

2) = 3a^2 This value should be equal to (b-2)/a So (b-2)/a = 3a^2 => b-2 = 3a^3 Sub back into y = 3x^3

we have 3a^3+2=a^3 2a^3 = -2 a = -1

b = -1 The touching point is (-1

-1) Equation of the tangent line is y - 2 = 3x or y - 3x - 2 = 0 2011-01-21 21:34:51 补充： thery are both the slopes of the same line

y = x^3 dy/dx = 3x^2 Let (h

k) be a point on the curve such that k = h^3 dy/dx = 3h^2 Equation of tangent: y - k = 3h^2 (x - h) When the tangent passes through the point (0

2)

the equation of tangent bees 2 - k = 3h^2 (0 - h) = - 3h^3 Converting (h

k) into (x

y)

we obtain 2 - y = - 3x^3 y = 3x^3 + 2

一声叹息：好男人真难找！

A modern-day proverb, bemoaning the difficulty of finding a suitable male partner

成语取自艾迪格林的歌名‘好男人难觅’，成曲于1918年，刊登在当年12月12日《韦恩堡周刊钢琴曲》专栏，赶在圣诞打折季以每份90美分发售。（Eddie Green(1896–1950)美国歌舞剧演员和作曲人）

This phrase was coined by Eddie Green , as the title of his song A Good Man Is Hard To Find This was composed in 1918 and first offered for sale as a piano roll in the Fort Wayne Journal-Gazette on 12th December that year (just in time for Christmas - a bargain at 90 cents):

       好男难觅

为什么受伤总是你，

当你心有所仪，他是你的白马王子，

你却发现，又是滥情高手花花公子。

你心忿忿，眼巴巴地望，

好男人是不是都死光？

如果你的男人还能要，

记着，早上抱抱，晚上唠唠，

恩恩爱爱，暮暮朝朝。

好男难觅，

好男难觅。

A good man is hard to find

You always get the other kind

Just when you think that he is your pal

You look for him and find him fooling 'round some other gal

Then you rave, you even crave

To see him laying in his grave

So, if your man is nice, take my advice and hug him in the morning, kiss him ev'ry night,

Give him plenty lovin', treat him right

For a good man nowadays is hard to find, a good man nowadays is hard to find

A similar though more general outlook was expressed in the Bible, Micah 7:2 (King James Version):

The good man is perished out of the earth: and there is none upright among men: they all lie in wait for blood; they hunt every man his brother with a net

We don't know if Eddie Green was an Old Testament scholar, but it seems unlikely that he got the line from Micah

a good man is hard to findThe best-known version of the song was recorded by Sophie Tucker, who adopted it as a signature tune She was a little more charitable in her delivery of the lyric and sang the second line as "You may get the other kind"

Sophie Tucker was born Sophie Kalish; she changed her name and adopted Tucker as a stage name following a brief marriage to Louis Tuck It is interesting to speculate whether she was influenced to use Tucker by the style of dress she often wore on stage - see best bib and tucker

In the good man/good woman stakes, men got in a pre-emptive strike in the 17th century Abraham Darcie's work The originall of idolatries, or the birth of heresies, 1624, includes this opinion:

"There is nothing more hard to find in this world than a good woman, a good Mule, and a good Goat, being three vnhappie beasts"

More recently, and in what must be one of the most convoluted titles ever to grace a bookstand, we have Jo Lynne Pool's 1995 book title - A Good Man Is Hard To Find Unless You Ask God To Be Head Of Your Search Committee