Class notes APPM 1350 2.1

2.1 Derivatives wed Rate of Change
heusell: If s(t) = position of un
velocity over [t., tz] is $(1)/(7)
object, then the average
F2-F
Oct: The instantaneous velocity of the object at time = a
is ne ilf)-5(a)
Exi s(t) = 1.5+9.8+-4.9+² Find velocity at t=t
I'm
x+4
+-4
Lim (+)-5(4) = 17
(1.5 +9.84 4.4+² ) 11.5 +4.8(4)-9-4(4)²)
=174
+-4
lim 4.8 (+-4) - 4.4 (+2-16) lin 9.8(+-4)-4.4 (+64) (+-4)
+74
+24
7-4
#4X (9.8-4.9(++))
T-A
Da of the Derivative
lini
Χ
x = ath
y = f(x)
Secunt line
Average rate of change
Difference quotient
taf
+-4
lim 4.8-4.9 (4+4) = -29.4 m/s
+24
Slope of the secont
line of y= xl ulay
(a,x] is f(x)= ca)
X-a
ath) - a)
h
Oct 1: The tangent line of y=fces of (a, feus) is the line through
6, few)) with slope in food-fcy) - live acht-feas - f'(a)
I'm f(x)-f(4)
X-a
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h
of
2: The sheet the curve of ga ces@
ga cas @ x=m is eas




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