69
Chapter 8: Applications of Derivatives
477. f
 
(x) = x
4
– 4x
2
+ 1
478. f
 
(x) = 2x
2
(1 – x
2
)
479. f x
x
x
( ) =
+
2
4
480. f
 
(x) = 2 sin x – x on [0, 2π]
Applying Rolle’s Theorem
481– 483 Verify that the function satisfies the
hypotheses of Rolle’s theorem. Then find all values
c in the given interval that satisfy the conclusion of
Rolle’s theorem.
481. f
 
(x) = x
2
–6x + 1, [0, 6]
482. f x x x
( ) =
+8, [–8, 0]
483. f
 
(x) = cos(2πx), [–1, 1]
470. f
 
(x) = 2 cos x – sin(2x) on [0, 2π]
Identifying Inflection Points
471–475 Find the inflection points of the given
function, if any.
471. f x x
x
( ) =
−
=
−
(
)
−
1
9
9
2
2
1
472. f
 
(x) = 2x
3
+ x
2
473. f x
x
x
( )
sin
cos
= +
1
on [0, 2π]
474. f
 
(x) = 3 sin x – sin
3 
x on [0, 2π]
475. f
 
(x) = x
5/3
– 5x
2/3
Using the Second Derivative
Test to Find Local Maxima
and Minima
476– 480 Use the second derivative test to find
the local maxima and local minima of the given
function.
476. f x
x
( ) =
+
(
)
2
2
3
1