Math Homework

My calc homework confuses me, please help.

Question:
y= x^2
y= - x^2 + 2x - 5

Find the equations of two lines that are simultaneously tangent to both parabolas.

y=2x+2.5

>>2
fail.


set the derivatives of the two eqns equal to each other, solve for x.

m = y'(x)  -- the x is the one you just solved for


plug in the same x into the two eqns. you will get 2 y's. the same x is the x0 below. the two y's are y0 below. plug x0 and y0 two times into the point slope eqn below. you will get two lines.

y - y0 = m (x - x0)

>>3
There is no m in the equation, what the fuck are you talking about?

dy/dx=2x=-2x+2 } x=1/2

Now what? There is no m in the equation, what the fuck are you talking about?

There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about? There is no m in the equation, what the fuck are you talking about?

>>4
gb2 school..

y' = dy/dx

m = dy/dx(x = 1/2) = 2*(1/2) = -2*(1/2)+2 = 1

>>4
The x value such that the derivatives are equal does not (necessarily) give the slope of a line which is tangent to both curves. The lines are 4x - 4 and -2x - 1. You find this by expressing a tangent to f(t) = t^2 (the first function) as a function of t and x (specifically, y = 2tx - t^2), then subtracting that from the second function and using the quadratic formula to find which values of t result in a double root (ie tangent line), then substituting those values of t back into y = 2tx - t^2 to get the line equations.

>>7
what? methinks you are trolling.

you got x = 1/2. slope = m = y'(1/2) = 1. then plug x into the two equations to get 2 y's, 1/4 and -21/4. then fill in the two point slope eqns to get the lines.

(1) y - 1/4 = 1 (x - 1/2)
y = x - 1/4

(2) y - (-21/4) = 1 (x - 1/2)
y = x - 23/4

>>8
He asked for the two lines which are simultaneously tangent to BOTH PARABOLAS. You gave two parallel lines which are each tangent to ONE PARABOLA. If you can't understand the difference, then please refrain from posting answers in math threads until you complete high school geometry.

>>9
Well I didn't know what simultaneously tangent was okay :[. The way you solve it not understandable. anyway, link: http://www.karlscalculus.org/twotangents.html