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.]
The point Q (-4,7) lies on the function f(x). Suppose f(x) is transformed according to: y=-3 f [0.5(x + 3)] + 5. Determine the x-coordinate of the transformed point, Q'. Enter only the x-coordinate, a single value, rounded correctly to 2 decimal places (ie 3.46 or 7.00 or 1.50)
3. Let f(x) = 8x- 3x*+5
%3!
a) Find where f has stationary points.
b) Perform a sign analysis on the derivative of f. Find where f is increasing and decreasing.
c) Use your results to find where all local maxima and minima of foccur.
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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