X2 t07 06 roots of functions (2012)

(I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0

y  f x
y

1

x

-1

and noticing;
 f  x   0 for all x in the domain
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1

and noticing;
 f  x   0 for all x in the domain
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1
dy f  x 
  implies;
dx f x

 stationary points must still be stationary points

 there are critical points where f  x   0

y  f x
y

y f x
1

x

-1

y

1
y 2  f x

x

-1

X2 t07 06 roots of functions (2012)

More Related Content

What's hot (10)

Similar to X2 t07 06 roots of functions (2012) (20)

More from Nigel Simmons (20)

Recently uploaded (20)

X2 t07 06 roots of functions (2012)