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Critical points, extrema and increasing intervals practice
Critical points, extrema and increasing intervals · 1–12
Use the first derivative to answer each question.
1.f(x) = −x3 − 272x2 − 60x − 1Find where f has a local maximum and a local minimum.
2.f(x) = −x3 + 92x2 − 1Find where f has a local maximum and a local minimum.
3.f(x) = −2x3 + 6x − 7Find where f has a local maximum and a local minimum.
4.f(x) = −2x3 + 12x2 − 18x + 3Find where f has a local maximum and a local minimum.
5.f(x) = 3x3 + 18x2 + 27x − 7Find where f has a local maximum and a local minimum.
6.f(x) = 2x3 + 15x2 + 24x − 4Find where f has a local maximum and a local minimum.
7.f(x) = 3x3 + 18x2 + 27x + 6Find where f has a local maximum and a local minimum.
8.f(x) = −x3 − 152x2 − 12x − 8Find where f has a local maximum and a local minimum.
9.f(x) = −x3 + 212x2 − 30x + 8Find where f has a local maximum and a local minimum.
10.f(x) = 3x3 − 27x2 + 72x + 2Find where f has a local maximum and a local minimum.
11.f(x) = 2x3 − 24x2 + 72x + 4Find where f has a local maximum and a local minimum.
12.f(x) = −2x3 − 12x2 − 1Find where f has a local maximum and a local minimum.
Answer key — Critical points, extrema and increasing intervals practice
Critical points, extrema and increasing intervals
1.local maximum at x = −4, local minimum at x = −5
2.local maximum at x = 3, local minimum at x = 0
3.local maximum at x = 1, local minimum at x = −1
4.local maximum at x = 3, local minimum at x = 1
5.local maximum at x = −3, local minimum at x = −1
6.local maximum at x = −4, local minimum at x = −1
7.local maximum at x = −3, local minimum at x = −1
8.local maximum at x = −1, local minimum at x = −4
9.local maximum at x = 5, local minimum at x = 2
10.local maximum at x = 2, local minimum at x = 4
11.local maximum at x = 2, local minimum at x = 6
12.local maximum at x = 0, local minimum at x = −4
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