Which conditions should the function follow to be bounded from below
$begingroup$
Let us consider that $f:mathbb{R}rightarrowmathbb{R}$ is a smooth function and $A, B$ are positive constants.
Let us define the function $g(x)$ given by:
$$
g(x) = -A f(x) + B f''(x).
$$
I wonder about conditions of $f(x)$ that makes $g(x)$ bounded from below.
For example if $f(x)$ is bounded from above and convex then of course $g(x)$ is bounded from below. But I want to find more general rules.
real-analysis calculus
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
$endgroup$
add a comment |
$begingroup$
Let us consider that $f:mathbb{R}rightarrowmathbb{R}$ is a smooth function and $A, B$ are positive constants.
Let us define the function $g(x)$ given by:
$$
g(x) = -A f(x) + B f''(x).
$$
I wonder about conditions of $f(x)$ that makes $g(x)$ bounded from below.
For example if $f(x)$ is bounded from above and convex then of course $g(x)$ is bounded from below. But I want to find more general rules.
real-analysis calculus
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
$endgroup$
add a comment |
$begingroup$
Let us consider that $f:mathbb{R}rightarrowmathbb{R}$ is a smooth function and $A, B$ are positive constants.
Let us define the function $g(x)$ given by:
$$
g(x) = -A f(x) + B f''(x).
$$
I wonder about conditions of $f(x)$ that makes $g(x)$ bounded from below.
For example if $f(x)$ is bounded from above and convex then of course $g(x)$ is bounded from below. But I want to find more general rules.
real-analysis calculus
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
$endgroup$
Let us consider that $f:mathbb{R}rightarrowmathbb{R}$ is a smooth function and $A, B$ are positive constants.
Let us define the function $g(x)$ given by:
$$
g(x) = -A f(x) + B f''(x).
$$
I wonder about conditions of $f(x)$ that makes $g(x)$ bounded from below.
For example if $f(x)$ is bounded from above and convex then of course $g(x)$ is bounded from below. But I want to find more general rules.
real-analysis calculus
real-analysis calculus
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
asked Dec 3 '18 at 17:28
MathMenMathMen
1267
1267
add a comment |
add a comment |
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