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.]
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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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