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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 + 32x2 − 60x + 3Find where f has a local maximum and a local minimum.
2.f(x) = −2x3 − 12x2 + 5Find where f has a local maximum and a local minimum.
3.f(x) = −x3 + 92x2 − 3Find where f has a local maximum and a local minimum.
4.f(x) = 3x3 + 36x2 + 135x − 4Find where f has a local maximum and a local minimum.
5.f(x) = −2x3 + 96x − 1Find where f has a local maximum and a local minimum.
6.f(x) = 2x3 − 24x − 9Find where f has a local maximum and a local minimum.
7.f(x) = 2x3 + 21x2 + 72x − 4Find where f has a local maximum and a local minimum.
8.f(x) = −x3 + 152x2 − 3Find where f has a local maximum and a local minimum.
9.f(x) = −2x3 + 15x2 + 6Find where f has a local maximum and a local minimum.
10.f(x) = x3 − 152x2 − 5Find where f has a local maximum and a local minimum.
11.f(x) = −2x3 + 54x + 2Find where f has a local maximum and a local minimum.
12.f(x) = x3 + 152x2 + 12x + 4Find 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 = −5, local minimum at x = 4
2.local maximum at x = 0, local minimum at x = −4
3.local maximum at x = 3, local minimum at x = 0
4.local maximum at x = −5, local minimum at x = −3
5.local maximum at x = 4, local minimum at x = −4
6.local maximum at x = −2, local minimum at x = 2
7.local maximum at x = −4, local minimum at x = −3
8.local maximum at x = 5, local minimum at x = 0
9.local maximum at x = 5, local minimum at x = 0
10.local maximum at x = 0, local minimum at x = 5
11.local maximum at x = 3, local minimum at x = −3
12.local maximum at x = −4, local minimum at x = −1
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