In Exercises 91–96 , the graph of a derivative f ′ is shown. Use the information in each graph to determine where f is increasing or decreasing and the x -values of any extrema. Then sketch a possible graph of f . Increasing on ( − 1 , ∞ ) , decreasing on ( − ∞ , − 1 ) , relative minimum at x = − 1 .
In Exercises 91–96 , the graph of a derivative f ′ is shown. Use the information in each graph to determine where f is increasing or decreasing and the x -values of any extrema. Then sketch a possible graph of f . Increasing on ( − 1 , ∞ ) , decreasing on ( − ∞ , − 1 ) , relative minimum at x = − 1 .
Solution Summary: The author analyzes the graph of the derivative function fprime and determines whether the function is decreasing or increasing.
In Exercises 91–96, the graph of a derivative
f
′
is shown. Use the information in each graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of
f
.
Increasing on
(
−
1
,
∞
)
, decreasing on
(
−
∞
,
−
1
)
, relative minimum at
x
=
−
1
.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Chapter 3 Solutions
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