So the
critical points are  x = 0 and 
x =81 Now evaluating the value of f at critical points
x = 0, 1
8  and at end points of the interval x = –1 and x = 1, we have
f (–1) =
4
1
3
3
12( 1)
6( 1)
18
−
−
−
=
f (0) = 12 (0) – 6(0) = 0
Rationalised 2023-24
 MATHEMATICS
174
f 81




  =
4
1
3
3
1
1
9
12
6
8
8
−4




−
=








f (1) =
4
1
3
3
12(1)
6(1)
6
−
=
Hence, we conclude that absolute maximum value of  f  is 18 that occurs at x = –1
and absolute minimum value of f is 
49
−  that occurs at 
x =81 Example 29 An Apache helicopter of enemy is flying along the curve given by
y = x2 + 7 A soldier, placed at (3, 7), wants to shoot down the helicopter when it is
nearest to him