Thomas Calculus 13th [Solutions]

186 Chapter 3 Derivatives
65. The values of f increase over the interval [ 1, 1] because f 0, and the graph of f steepens as the values of
f increase towards the ends of the interval. The graph of f is concave down to the left of the origin where
f 0, and concave up to the right of the origin where f 0. There is an inflection point at x = 0 where
f 0 and f has a local minimum value.
66. The values of f increase throughout the interval ( , ) because f 0, and they increase most rapidly near
the origin where the values of f are relatively large. The graph of f is concave up to the left of the origin
where f 0, and concave down to the right of the origin where f 0. There is an inflection point at x = 0
where f 0 and f has a local maximum value.
3.10 RELATED RATES
1.
2.
2
A r dA 2 r dr
dt dt
2
S 4 r dS 8 r dr
dt dt
dy
dy
3. y 5 x, dx 2 5 dx 5(2) 10
dt dt dt dt
dy
4. 2x 3y 12, 2 2 dx dy
3 0 2 dx 3( 2) 0 dx 3
dt
dt dt dt dt
Copyright
2014 Pearson Education, Inc.