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Rates of Change of Polynomials
Related Topics
Wize High School Grade 12 Pre-Calculus Textbook > Rates of Change
Rates of Change of Polynomials
5 Activities
Practice: Rates of Change of Polynomials
Let
f
(
x
)
=
x
3
−
x
+
1
f(x)=x^3-x+1
f
(
x
)
=
x
3
−
x
+
1
.
a. Estimate the slope of the tangent line at
x
=
1
x=1
x
=
1
. Let
h
=
0.001
h=0.001
h
=
0.001
. (Round to nearest thousandth)
b. Find the
y
y
y
-coordinate at the point of tangency.
c. Determine the equation of the tangent line
y
=
y=
y
=
I don't know
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More Rates of Change of Polynomials Questions:
Average & Instantaneous Rate of Change
The position of an object is given by
d
(
t
)
=
3
t
3
−
4
t
+
1
d(t)=3t^3-4t+1
d
(
t
)
=
3
t
3
−
4
t
+
1
where
d
d
d
is in meters and
t
t
t
is in minutes.
What is the average rate of change between t=1 and t=2
? Round to the nearest whole number, do not include units.
Average & Instantaneous Rate of Change
The position of an object is given by
d
(
t
)
=
3
t
3
−
4
t
+
1
d(t)=3t^3-4t+1
d
(
t
)
=
3
t
3
−
4
t
+
1
where
d
d
d
is in meters and
t
t
t
is in minutes.
Rates of Change of Polynomials
Practice: Rates of Change of Polynomials
Let
f
(
x
)
=
x
2
−
4
f(x)=x^2-4
f
(
x
)
=
x
2
−
4
.
Estimate the tangent lines at the x-intercepts to the nearest whole number. (Use
h
=
0.001
h=0.001
h
=
0.001
)
Rates of Change of Polynomials
Practice: Rates of Change of Polynomials
Let
f
(
x
)
=
±
−
x
f(x)=\pm\sqrt{-x}
f
(
x
)
=
±
−
x
.
Estimate the tangent lines at the point
x
=
−
2
x=-2
x
=
−
2
. Round to the nearest hundredth. (Use
h
=
0.001
h=0.001
h
=
0.001
)
Rates of Change of Polynomials
Practice: Rates of Change of Polynomials
Let
f
(
x
)
=
3
x
2
+
2
x
−
8
f(x)=3x^2+2x-8
f
(
x
)
=
3
x
2
+
2
x
−
8
.
Rates of Change of Polynomials
Practice: Rates of Change of Polynomials
Let
f
(
x
)
=
7
x
5
−
4
x
+
9
f(x)=7x^5-4x+9
f
(
x
)
=
7
x
5
−
4
x
+
9
be a continuous polynomial function over the interval
(
−
∞
,
∞
)
.
(-\infin,\infin).
(
−
∞
,
∞
)
.
Determine the following:
Rates of Change of Polynomials
Practice: Rates of Change of Polynomials
Let
f
(
x
)
=
2
x
2
+
x
−
5
f(x)=2x^2+x-5
f
(
x
)
=
2
x
2
+
x
−
5
be a continuous polynomial function over the interval
(
−
∞
,
∞
)
.
(-\infin,\infin).
(
−
∞
,
∞
)
.
Determine the following: