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The derivative of mathematical problem y ^ 2 = 2px, find a subscript x of Y 'and find the tangent equation of parabola in (X., Y.) Is this 2yy '= 2p?
y^2=2px
2yy'=2p
y'=p/y
Tangent equation y-y. = P / y. (X-X.)
That is y = P / y. (X-X.) + y
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The two sides are deriving x at the same time
Derivation of implicit function
It is known that the tangent slope of the parabola y equal to ax at x = 1 is two. The equation of the parabola is solved. The tangent equation of ＜ 1. - 3 ＞ is solved
f(x)=ax^2
f'(x)=2ax
According to the meaning f '(1) = 2A = 2, a = 1 is obtained
Parabolic equation f (x) = x ^ 2
(1, - 3) not on parabola
The tangent point is on the parabola, let the tangent point be (x0, x0 ^ 2)
(x0^2-(-3))/(x0-1)=2x0
x0^2+3=2x0^2-2x0
x0^2-2x0-3=0
(x0+1)(x0-3)=0
The two tangent points are (- 1,1) (3,9)
Point oblique
(y-1)/(x-(-1))=-2
y=-2x-1
(y-9)/(x-3)=6
y=6x-9
The tangent equation is y = - 2x-1 or y = 6x-9
The slope of the tangent of the parabola y = x * x + X + 1 at point x = 0 is
1
Cubic parabola y = x ^ 3 at point M1__ Sum point M2__ The slopes of the tangents at are all equal to 3,
The underscores are the two blanks that let you fill in
y‘=3x²=3=>x=±1
So: M1 (- 1, - 1), M2 (1,1)
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