Horizontal tangents and normals to curves

[][nstigator]

Im havin some real problems with my maths :( I am behidn coz I went on a holiday for easter. I have a test tomorrow and I really need help

If anyone could teach me how to do these sort of questions it would be much appreciated.

1. Find all points of contact of horizontal tangents to the curve
y=2√x+1/√x

2. Find equation of tangent to
y=1-3x+12x²-8x³
which is parallel to the tangent at (1,2)

3. The normal to the curve
y=a√x+b/√x
where a and b are constants, has equation 4x+y=22 at the point where x=4. Find the values of a and b.

I haven't had much trouble with other work in the chapter, but I have continously got questions similar to this wrong. Some help would be much appreciated.

 

[Berislav]

1. $$y'=0$$

The solve for x.

2. $$y'(1) = y' (x)$$

Find x.

3. 4x+y=22, from which k=-4, from which $k_t=1/4$ From which $y' (4) = 0.25.$

Edit:

In 2. After you find the point of interest. Find the value of the derivative there, this will equal k (y=kx+l) of the tangent. It is simple then to find l.

 

[][nstigator]

I don't quite understand 2 :(

and where do u get k from?!

 

[][nstigator]

I don't quite understand 2 :(

Editops soz, ment to edit and get rid of the part where I said "where do u get k from"

Edit2: aw crap, I still have no idea for those questions

 

[Berislav]

The k (y=kx+l) of a tangent of a curve at a certain point is equal to the value of the derivative of the curve at that point. After solving the equation, you will get an x or two that satisfy it. Find the value of the derivative at those points. Find the l's by satisfying that the tangents intersect with the curve at that point.