In Exercises 29–32 the graph of the second derivative, f ″ ( x ) , is given. Determine the x-coordinates of all points of inflection of f ( x ) , if any. (Assume that f ( x ) is defined and continuous everywhere in [ − 3 , 3 ] .) [ HINT: Remember that a point of inflection of f corresponds to a point at which f ″ schanges sign, from positive to negative or vice versa. This could be a point where its graph crosses the x -axis or a point where its graph is broken: positive on one side of the break and negative on the other.]
In Exercises 29–32 the graph of the second derivative, f ″ ( x ) , is given. Determine the x-coordinates of all points of inflection of f ( x ) , if any. (Assume that f ( x ) is defined and continuous everywhere in [ − 3 , 3 ] .) [ HINT: Remember that a point of inflection of f corresponds to a point at which f ″ schanges sign, from positive to negative or vice versa. This could be a point where its graph crosses the x -axis or a point where its graph is broken: positive on one side of the break and negative on the other.]
Solution Summary: The author explains the x -coordinates of the point of inflection of a function.
In Exercises 29–32 the graph of the second derivative,
f
″
(
x
)
, is given. Determine the x-coordinates of all points of inflection of
f
(
x
)
, if any. (Assume that
f
(
x
)
is defined and continuous everywhere in
[
−
3
,
3
]
.) [HINT: Remember that a point of inflection of f corresponds to a point at which
f
″
schanges sign, from positive to negative or vice versa. This could be a point where its graph crosses the x-axis or a point where its graph is broken: positive on one side of the break and negative on the other.]
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.
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY