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5.3 Concavity and Inflection Points. Section 1: Determine the open intervals on which the graph s concave up or concave down. f (x) = 24 x2 + 12. f (x) = x2 + 1 x2 − 1. y = 2x − tan x π π , (− 2 ) Section 2: Find the inflection points and the open intervals of concavity.
Dec 21, 2020 · If we are trying to understand the shape of the graph of a function, knowing where it is concave up and concave down helps us to get a more accurate picture. Of particular interest are points at which the concavity changes from up to down or down to up; such points are called inflection points.
A series of free Calculus Videos and solutions. Concavity Practice Problem 1. Problem: Determine where the given function is increasing and decreasing. Find where its graph is concave up and concave down. Find the relative extrema and inflection points and sketch the graph of the function. f (x)=x^5-5x Concavity Practice Problem 2.
If we are trying to understand the shape of the graph of a function, knowing where it is concave up and concave down helps us to get a more accurate picture. Of particular interest are points at which the concavity changes from up to down or down to up; such points are called inflection points .
Increasing and Decreasing Functions, Concavity 1. Suppose f(x) = (x 31)(x 4)(x 9) = x 14x2 + 49x 36: (a) Find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. (b) Find the intervals on which f(x) is concave up and the intervals on which f(x) is concave down. 2. Suppose g0(x) = (x 1)(x 4)(x 9) = x3 14x2 ...
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Why does a function h concave up and down?
Concave up because the rate of change is increasing over equal‐length input‐value intervals. Concave down because the rate of change is decreasing over equal‐length input‐value intervals.
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