January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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5.6 Applications of Derivative
Functions: f, g, y
Position of an object: s
Velocity: v
Acceleration: w
Independent variable: x
Time: t
Natural number: n
G
Velocity and acceleration
s 5 f(t) is the position of an object relative to a fixed coordinate system at a time t,
v 5 s
0
5 f
0
(t) is the instantaneous velocity of the object, w 5 v
0
5 sv 5 fv(t) is the instantaneous
acceleration of the object.
G
Tangent line: y 2 y
0
5 f
0
(x
0
)(x 2 x
0
).
G
Normal line:
y 2 y
0
52
1
f
0
ðx
0
Þ
ðx 2 x
0
Þ
G
Increasing and decreasing functions:
If f
0
(x
0
) . 0, then f(x) is increasing at x
0
.
If f
0
(x
0
) , 0, then f(x) is decreasing at x
0
.
If f
0
(x
0
) does not exist or is zero, then the test fails.
G
Local ...
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