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Concavity and inflection points practice
Concavity and inflection points · 1–12
Use the second derivative to answer each question.
1.f(x) = −x4 + 96x2 + 3x + 7Find the x-coordinates of the inflection points.
2.f(x) = −x4 + 10x3 − 36x2 − 2x + 9Find the x-coordinates of the inflection points.
3.f(x) = −x4 − 6x3 − 2x − 1Find the x-coordinates of the inflection points.
4.f(x) = −x4 + 6x2 + 5x − 2Find the x-coordinates of the inflection points.
5.f(x) = −x4 − 18x3 − 108x2 + 5x − 2Find where f is concave up and where it is concave down.
6.f(x) = x4 − 24x2 − 7x + 3Find where f is concave up and where it is concave down.
7.f(x) = x4 − 12x3 + 48x2 − 7x + 8Find where f is concave up and where it is concave down.
8.f(x) = x4 + 8x3 − x + 4Find the x-coordinates of the inflection points.
9.f(x) = x4 − 4x3 + x − 8Find the x-coordinates of the inflection points.
10.f(x) = −x4 + 2x3 + 36x2 − 4x + 4Find the x-coordinates of the inflection points.
11.f(x) = x4 − 4x3 − 18x2 − 5x − 9Find the x-coordinates of the inflection points.
12.f(x) = x4 − 2x3 + x + 4Find where f is concave up and where it is concave down.
Answer key — Concavity and inflection points practice
Concavity and inflection points
5.concave up for −6 < x < −3; concave down for x < −6 and for x > −3
6.concave up for x < −2 and for x > 2; concave down for −2 < x < 2
7.concave up for x < 2 and for x > 4; concave down for 2 < x < 4
12.concave up for x < 0 and for x > 1; concave down for 0 < x < 1
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