Concave up and concave down? - Mathematics Stack Exchange
Mar 30, 2016 · 2 I am unable to find out how to find concave up and concave down just by looking at a graph of function f(x) f (x). I was told that if the tangent line of the slope can be visualized under the …
calculus - Why is it necessary to take the 2nd derivative to determine ...
Jul 18, 2021 · Just because it's concave-up to the left & right of 0 doesn't mean it's concave up at 0. Unlike y=x^2 and despite appearances on a graphing calc, y=x^4 is truly "flat" (neither conc-up nor …
Find the intervals where f is concave upwards and downwards, and ...
Mar 1, 2020 · So the graph is concave down in the interval $2<x<3$. For a smooth graph (do you know what this means?) an inflection point always lies between concave up and concave down segments.
Concave down increasing example - Mathematics Stack Exchange
I'm looking for a concave down increasing -function, see the image in the right lower corner. Basically I need a function f(x) which will rise slower as x is increasing. The x will be in range of [0.10 .. 10], so …
I'm asked to find the intervals of a graph where f is concave down. I ...
Dec 9, 2022 · The function is concave down when the second derivative is negative. Since you're given the derivative, you want the intervals where the derivative of the derivative is negative, i.e. the …
How to remember which function is concave and which one is convex?
If you know the standard English meaning of the words convex and concave, you can remember that for a convex function it is the epigraph that is convex, and for a concave function it is the epigraph that is …
How to determine the interval where $f(x)$ is concave up and concave …
Sep 19, 2020 · But graphs being concave up/down is determined entirely by the sign of f′′(x) f ″ (x), so whether the gradient itself is decreasing or increasing (so whether growth slows down or increases).
Why does "convex function" mean "concave *up*"?
But then concave up should equal convex down, i.e., the curve is the top (up) part of a concave region. Concave down then equals convex up, meaning that the curve is lower part of a concave epigraph or …
Solved Consider the following. (If an answer does not exist ... - Chegg
Math Calculus Calculus questions and answers Consider the following. (If an answer does not exist, enter DNE.) f (x)=ln (2+sin (x)),0≤x≤2π Find the interval (s) on which f is concave up. (Enter your …
calculus - How does the second derivative imply concavity ...
Jan 3, 2018 · That makes the graph concave up. So the 2nd derivative tells you which way the tangent line is rotating; either counter-clockwise (positive) or clockwise (negative.) This rotation tells you …