For Exercises 67-68, find the constants A and B so that the two polynomials are equal. (Hint: Create a system of linear equations by equating the constant terms and by equating the coefficients on the x terms and x 2 terms.) 11 x 2 + 26 x − 5 = 2 A x 2 + 5 A x + 3 A + B x 2 − 2 B x − 8 B + 2 C x 2 − 7 C x − 4 C
For Exercises 67-68, find the constants A and B so that the two polynomials are equal. (Hint: Create a system of linear equations by equating the constant terms and by equating the coefficients on the x terms and x 2 terms.) 11 x 2 + 26 x − 5 = 2 A x 2 + 5 A x + 3 A + B x 2 − 2 B x − 8 B + 2 C x 2 − 7 C x − 4 C
Solution Summary: The author explains how to calculate the constants, A and B, such that the polynomial is satisfied, and creates a system linear equation by equating the coefficients in the
For Exercises 67-68, find the constants
A
and
B
so that the two polynomials are equal. (Hint: Create a system of linear equations by equating the constant terms and by equating the coefficients on the
x
terms and
x
2
terms.)
11
x
2
+
26
x
−
5
=
2
A
x
2
+
5
A
x
+
3
A
+
B
x
2
−
2
B
x
−
8
B
+
2
C
x
2
−
7
C
x
−
4
C
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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