Page 299 - Calculus Demystified

Solutions to Exercises
286
√
Thus there are a critical point at x = 0 and inflection points at x =±1/ 3.
Figure S3.15 exhibits the complete graph.

Fig. S3.15

16. We see that the equation for the position of a falling body will now be
20
2
p(t) =− t + v 0 t + h 0 .
2
It is given that v 0 = 0 and h 0 = 100. Hence
2
p(t) =−10t + 0t + 100.
The body hits the surface when
2
0 = p(t) =−10t + 100.
√
This occurs at time t = 10.
Chapter 4

3
1. (a) F(x) = x /3 + cos x + C
5
3x
(b) F(x) = e /3 + x /5 − 2x + C
3
2
(c) F(t) = t +[ln t] /2
(d) F(x) =− ln(cos x) − sin x −[cos 3x]/3 + C
(e) F(x) =[sin 3x]/3 −[cos 4x]/4 + x + C
(f) F(x) = e sin x + C
− cos x 2
2
2. (a) x sin x dx = + C
2