Absolute Maximum

1
2.8 Geometrical Application of Calculus
Absolute Maximum Minimum

• The maximum and minimum turning points may not be
  the maximum and minimum for the function.

• They may be called relative or local maximum or
  minimums.

• If we restrict the domain (-4 x 4) then we
  can have an absolute max or min.

• It is possible that the relative or local value
  could be the same as the absolute value.

2
2.8 Geometrical Application of Calculus
Absolute Maximum Minimum

• Find the maximum and minimum value for y when y
  2x3 - 3x2 2 for -1 x 2

f(x) 6x2 - 6x
f(0) 2(0)33(0)22 2
Stationary points when 6x2 - 6x 0
f(1) 2(1)33(1)22 1
6x(x 1) 0
Stationary points at (0,2) and (1,1).
x 0 or x 1