In Exercises 1–6, (a) state the values of a, b, and c in the given quadratic function f ( x ) = a x 2 + b x + c ; (b) supply the missing values in the table below; (c) calculate f ( a + h ) ; and (d) give a valid technology formula for f ( x ) . (Optional: Use technology to check the values in the table.) [ HINT: See Quick Examples 1–3.] x –3 –2 –1 0 1 2 3 f ( x ) f ( x ) = 2 x 2 − x − 2
In Exercises 1–6, (a) state the values of a, b, and c in the given quadratic function f ( x ) = a x 2 + b x + c ; (b) supply the missing values in the table below; (c) calculate f ( a + h ) ; and (d) give a valid technology formula for f ( x ) . (Optional: Use technology to check the values in the table.) [ HINT: See Quick Examples 1–3.] x –3 –2 –1 0 1 2 3 f ( x ) f ( x ) = 2 x 2 − x − 2
Solution Summary: The author explains that a quadratic equation or function is expressed in function form as well as in equation form.
In Exercises 1–6, (a)state the values of a, b, and c in the given quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
c
; (b)supply the missing values in the table below;(c)calculate
f
(
a
+
h
)
; and(d)give a valid technology formula for
f
(
x
)
. (Optional: Use technology to check the values in the table.) [HINT: See Quick Examples 1–3.]
Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z²
= x²+
+12
x
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
2z
dz
dt
dx
2x.
+2y
dt
dx
dy
dz
x
+y
dt
dt
dt
2z
dy
dt
×
dx
(x+y
dt
dy
dt
An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters.
9
ground level
Assume that x is increasing at a rate of 3 meters/sec.
(a) Write as a function of x: 0=
(b) When x=10, the angle is changing at a rate of
rad/sec.
(c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R?
○ Yes
○ No
4.1 Basic Rules of Differentiation.
1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with
appropriate derivative notation.
a) y=8x-5x3 4
X
b)
y=-50 √x+11x
-5
c) p(x)=-10x²+6x3³
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