Increasing, decreasing and concavity practice problems
Sign charts for f′ and f″: where a graph rises, falls, and bends. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.
For \( \displaystyle f(x) = 3 x^{3} + 18 x^{2} + 27 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} - 18 x^{2} + 48 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - \frac{27 x^{2}}{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - \frac{3 x^{2}}{2} - 18 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - 36 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - 9 x^{2} - 27 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} + 27 x^{2} + 72 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} + 3 x^{2} - 9 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} + \frac{27 x^{2}}{2} - 36 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - \frac{15 x^{2}}{2} + 12 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - \frac{9 x^{2}}{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} + 15 x^{2} + 24 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} - 9 x^{2} - 24 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} + 3 x^{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} - 3 x^{2} - 36 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} + 9 x^{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - \frac{27 x^{2}}{2} + 18 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - 9 x^{2} - 72 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} - 9 x^{2} + 12 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} + \frac{21 x^{2}}{2} + 36 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} - 6 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - 6 x^{2} + 9 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - 6 x^{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} + 15 x^{2} + 36 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - 3 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} + 3 x^{2} - 12 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 3 x^{3} - \frac{45 x^{2}}{2} + 36 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - \frac{9 x^{2}}{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = x^{3} - \frac{15 x^{2}}{2} + 18 x \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.
For \( \displaystyle f(x) = 2 x^{3} - 6 x^{2} \), find the intervals where f is increasing or decreasing, where it is concave up or down, and its inflection points.