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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) = −x3 + 6x2 − 3x + 2Find where f is concave up and where it is concave down.
2.f(x) = −2x3 + 18x2 − 2x + 3Find where f is concave up and where it is concave down.
3.f(x) = 2x3 − 4x + 1Find where f is concave up and where it is concave down.
4.f(x) = −2x3 + 6x2 + 7x + 9Find where f is concave up and where it is concave down.
5.f(x) = −2x3 − 6x2 − 6x − 3Find where f is concave up and where it is concave down.
6.f(x) = −2x3 − 12x2 − 3x + 3Find where f is concave up and where it is concave down.
7.f(x) = 2x3 + 18x2 − 7xFind where f is concave up and where it is concave down.
8.f(x) = −2x3 + 2x − 9Find where f is concave up and where it is concave down.
9.f(x) = −x3 − 4x + 9Find where f is concave up and where it is concave down.
10.f(x) = 2x3 − 6x2 + 4x − 6Find where f is concave up and where it is concave down.
11.f(x) = −x3 − 6x2 + 5x − 4Find where f is concave up and where it is concave down.
12.f(x) = −x3 − 3x2 + 7x − 7Find where f is concave up and where it is concave down.
Answer key — Concavity and inflection points practice
Concavity and inflection points
1.concave up for x < 2; concave down for x > 2
2.concave up for x < 3; concave down for x > 3
3.concave up for x > 0; concave down for x < 0
4.concave up for x < 1; concave down for x > 1
5.concave up for x < −1; concave down for x > −1
6.concave up for x < −2; concave down for x > −2
7.concave up for x > −3; concave down for x < −3
8.concave up for x < 0; concave down for x > 0
9.concave up for x < 0; concave down for x > 0
10.concave up for x > 1; concave down for x < 1
11.concave up for x < −2; concave down for x > −2
12.concave up for x < −1; concave down for x > −1
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