quiz 2 solution see quiz link. quiz 4 (in class) material: 2.6 saturday: 12 oct 2010
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QUIZ 2 solution
See Quiz link
QUIZ 4
(IN class)
Material: 2.6
Saturday: 12 oct 2010
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
Example:Find the derivative of the function at x = 2. Find
982)( xxxf)2('f
Example:Find the derivative of the function at a. Find
982)( xxxf)(' af
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
Example:Find the derivative of the function at a. Find )(' af
2
1)( )29
xxf
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
axhhax If
axh approaches 0 approaches
an equivalent way of stating the definition of the derivative
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
)(' afThe slope of the tangent line at the point (a,f(a))
Tangent line at x=3
Slope of this line )(' af
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
RATES OF CHANGE
xy on depends suppose
f(x)y
21
21
yy
xx
12
12
yyy
xxx
Chane in x =
Chane in y =
increment in x
average rate of change of y with respect to x over the interval [x1,x2] x
y
12
12
12
12 )()(
xx
xfxf
xx
yy
x
y
x= time, y = distanceaverage velocity
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
RATES OF CHANGE
average rate of change of y with respect to x over the interval [x1,x2] x
y
12
12
12
12 )()(
xx
xfxf
xx
yy
x
y
12 xx 0x
instantaneous rate of change =
x
yx
0lim
12
12 )()(lim
12 xx
xfxfxx
x= time, y = distanceinstantaneous velocity
Sec 2.7: DERIVATIVES AND RATES OF CHANGE
RATES OF CHANGE
average rate of change of y with respect to x over the interval [x1,x2] x
y
12
12
12
12 )()(
xx
xfxf
xx
yy
x
y
12 xx 0x
instantaneous rate of change =
x
yx
0lim
12
12 )()(lim
12 xx
xfxfxx
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H
R
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H
R
RH(a,b)
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H
H
H
H
R
R
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
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