68 Part I: The Questions
462. f x x
x
( ) = −8
463. f
 
(x) = 6x
2/3
– x
464. f
 
(x) = 2 sin x – sin 2x on [0, 2π]
465. f
 
(x) = x + 2 cos x on [–2π, 2π]
Determining Concavity
466– 470 Find the intervals where the given function
is concave up and concave down, if any.
466. f
 
(x) = x
3
– 3x
2
+ 4
467. f
 
(x) = 9x
2/3
– x
468. f
 
(x) = x
1/3
(x + 1)
469. f
 
(x) = (x
2
– 4)
3
Finding Intervals of Increase
and Decrease
456– 460 Find the intervals of increase and
decrease, if any, for the given function.
456. f
 
(x) = 2x
3
– 24x + 1
457. f x x x
( ) =
+3, x ≥ – 3
458. f
 
(x) = cos
2 
x – sin x on [0, 2π]
459. f
 
(x) = 2 cos x – cos 2x on 0 ≤ x ≤ 2π
460. f
 
(x) = 4 ln x – 2x
2
Using the First Derivative Test
to Find Local Maxima and
Minima
461– 465 Use the first derivative to find any local
maxima and any local minima.
461. f
 
(x) = 2x
3
– 3x
2
– 12x