Cobby's Methods Questions

[dekoyl]

Add them together


=

[cobby]

Sweet..thanks!!!

[Flaming_Arrow]

Thanks dekoyl...i got that answer too..

but the book says..

thats the same thing, they got a common denominator in that 1

[cobby]

Hey guys another q please

Consider the function where

a) Find the derivative of with respect to   - DONE
b) Find the coordinates of the stationary points of the graph of - DONE
c) Show that the stationary point at (1,0) is always a local maximum - NO CLUE WHAT THAT MEANS!?
d) Find the value of if the stationary points occur where x = 1 and x = 4 - Not Done



Thanks guys

[dekoyl]

I haven't done these in a while but for C, maybe do a sign diagram (/ at 0, _ at 1, \ at 2 => local maximum)?
Not sure if this satisfies the ALWAYS LOCAL MAXIMUM, though.

=(

[cobby]

I haven't done these in a while but for C, maybe do a sign diagram (/ at 0, _ at 1, \ at 2 => local maximum)?
Not sure if this satisfies the ALWAYS LOCAL MAXIMUM, though.

=(

Yeh when they mentiond 'always' thats threw me off course a bit..

[kamil9876]

I haven't done these in a while but for C, maybe do a sign diagram (/ at 0, _ at 1, \ at 2 => local maximum)?
Not sure if this satisfies the ALWAYS LOCAL MAXIMUM, though.

=(

Yeh when they mentiond 'always' thats threw me off course a bit..

'always' means for any value of b>1. So you would have to show that if b>1, dy/dx<0 when x>1 and 0<dy/dx when x<1. This is because positive gradient implies increasing, negative implies decreasing and so the gradient must be positive before x=1 and negative after x=1 in order for it to be max at x=1.

[cobby]

Straight line pass through the point B (1,-2) and is (are) tangent to the parabola with equation
Point A is on the parabola


1a) Show that the line is passing through point AB is given by
         

b)Show that the x co-ordinate of A is given by the solution to equation:
     

c) Hence show that:

d) Hence find the x and y co-ordinates - dont worry about this

e) Hence find the equations of the straight lines




Could someone please answer this...its for my SAC preparation ...

Thanks    

[kamil9876]

a.)
y=mx+c
subbing in B:
-2=m+c
c=-2-m
=-(2+m)

b.)
A is (x,y)

m=gradient



:

[Flaming_Arrow]

1a)




b)








c)

a= 1 b = m c = m+2







e)


solve for m and sub into equation in part a

[cobby]

Thank you so much guys!!

[cobby]

Hey guys got another question


For the curve with equation , calculate the possible values of k such that the tangents at the points with x-coordinates and respectively are perpendicular.

[Flaming_Arrow]

let x = 1



let







you can do it from there

[cobby]

Another one guys


Show that

Thanks!!

[Flaming_Arrow]