Name ______________________Date ____________Score ____ / 12
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 − 15x2 + 72x + 8Find where f is increasing and where it is decreasing.
2.f(x) = −2x3 − 15x2 − 4Find where f is increasing and where it is decreasing.
3.f(x) = 3x3 − 632x2 + 90x + 2Find where f is increasing and where it is decreasing.
4.f(x) = x3 + 32x2 − 6x − 2Find where f is increasing and where it is decreasing.
5.f(x) = 2x3 + 15x2 + 1Find where f is increasing and where it is decreasing.
6.f(x) = 2x3 − 24x − 7Find where f is increasing and where it is decreasing.
7.f(x) = x3 + 92x2 + 8Find where f is increasing and where it is decreasing.
8.f(x) = −x3 − 3x2 + 45x − 5Find where f is increasing and where it is decreasing.
9.f(x) = x3 − 92x2 − 30x − 2Find where f is increasing and where it is decreasing.
10.f(x) = x3 + 92x2 − 4Find where f is increasing and where it is decreasing.
11.f(x) = −2x3 − 15x2 − 24x − 7Find where f is increasing and where it is decreasing.
12.f(x) = −2x3 − 9x2 − 12x + 8Find where f is increasing and where it is decreasing.
Answer key — Critical points, extrema and increasing intervals practice
Critical points, extrema and increasing intervals
1.increasing for x < 4 and for x > 6; decreasing for 4 < x < 6
2.increasing for −5 < x < 0; decreasing for x < −5 and for x > 0
3.increasing for x < 2 and for x > 5; decreasing for 2 < x < 5
4.increasing for x < −2 and for x > 1; decreasing for −2 < x < 1
5.increasing for x < −5 and for x > 0; decreasing for −5 < x < 0
6.increasing for x < −2 and for x > 2; decreasing for −2 < x < 2
7.increasing for x < −3 and for x > 0; decreasing for −3 < x < 0
8.increasing for −5 < x < 3; decreasing for x < −5 and for x > 3
9.increasing for x < −2 and for x > 5; decreasing for −2 < x < 5
10.increasing for x < −3 and for x > 0; decreasing for −3 < x < 0
11.increasing for −4 < x < −1; decreasing for x < −4 and for x > −1
12.increasing for −2 < x < −1; decreasing for x < −2 and for x > −1
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