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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 + 12x2 + 7x + 8Find where f is concave up and where it is concave down.
2.f(x) = 2x3 − 12x2 + 7x − 4Find where f is concave up and where it is concave down.
3.f(x) = x3 + 9x2 − 9x + 4Find where f is concave up and where it is concave down.
4.f(x) = −2x3 − 12x2 − 5x − 2Find where f is concave up and where it is concave down.
5.f(x) = −2x3 + 6x2 − x − 4Find where f is concave up and where it is concave down.
6.f(x) = 2x3 + 12x2 − 3x + 1Find where f is concave up and where it is concave down.
7.f(x) = x3 + 9x2 + 7x + 4Find where f is concave up and where it is concave down.
8.f(x) = x3 − 12x2 + 6x + 1Find where f is concave up and where it is concave down.
9.f(x) = 2x3 + 6x2 − 2x − 1Find where f is concave up and where it is concave down.
10.f(x) = 2x3 − 3x − 4Find where f is concave up and where it is concave down.
11.f(x) = x3 + 6x2 − 9x − 4Find where f is concave up and where it is concave down.
12.f(x) = −x3 + 3x2 + 6x − 4Find 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 > −4; concave down for x < −4
2.concave up for x > 2; concave down for x < 2
3.concave up for x > −3; concave down for x < −3
4.concave up for x < −2; concave down for x > −2
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 > 4; concave down for x < 4
9.concave up for x > −1; concave down for x < −1
10.concave up for x > 0; concave down for x < 0
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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