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Critical numbers practice problems

Where f′ is zero or undefined: the candidates for maxima and minima. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Find the critical numbers of \( \displaystyle f(x) = x^{3} - \frac{3 x^{2}}{2} - 18 x - 2 \).
Problem 3.31easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} + 3 x^{2} - 72 x + 5 \).
Problem 3.32easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 2 x^{3} - 9 x^{2} + 60 x - 4 \).
Problem 3.33easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - x^{3} - 6 x^{2} + 15 x + 2 \).
Problem 3.34easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} + 6 x^{2} - 18 x - 5 \).
Problem 3.35easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = x^{3} - 3 x^{2} - 24 x + 2 \).
Problem 3.36easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - x^{3} + 6 x^{2} + 1 \).
Problem 3.37easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - x^{3} + 6 x^{2} + 15 x - 2 \).
Problem 3.38easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = x^{3} - 3 x + 5 \).
Problem 3.39easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 3 x^{3} + 9 x^{2} - 72 x + 1 \).
Problem 3.40easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} + 3 x^{2} - 36 x + 1 \).
Problem 3.41easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 2 x^{3} - 27 x^{2} - 120 x + 5 \).
Problem 3.42easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 3 x^{3} + \frac{81 x^{2}}{2} + 180 x + 4 \).
Problem 3.43easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 2 x^{3} + 3 x^{2} + 2 \).
Problem 3.44easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} - 24 x^{2} + 90 x - 1 \).
Problem 3.45easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} + 3 x^{2} - 120 x + 3 \).
Problem 3.121easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = x^{3} - \frac{3 x^{2}}{2} - 18 x - 4 \).
Problem 3.122easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 2 x^{3} + 24 x - 5 \).
Problem 3.123easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 3 x^{3} + \frac{9 x^{2}}{2} + 180 x - 1 \).
Problem 3.124easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 2 x^{3} - 3 x^{2} + 12 x + 3 \).
Problem 3.125easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 3 x^{3} + 81 x + 3 \).
Problem 3.126easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} - 12 x^{2} + 18 x - 1 \).
Problem 3.127easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = 2 x^{3} + 9 x^{2} + 12 x - 5 \).
Problem 3.128easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 3 x^{3} + 27 x^{2} - 45 x \).
Problem 3.129easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = x^{3} - 27 x - 4 \).
Problem 3.130easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - x^{3} - \frac{9 x^{2}}{2} + 30 x + 2 \).
Problem 3.131easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - x^{3} - 6 x^{2} - 4 \).
Problem 3.132easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 3 x^{3} + 144 x \).
Problem 3.133easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - x^{3} + 3 x^{2} + 9 x \).
Problem 3.134easy✓ Every equation proved
Find the critical numbers of \( \displaystyle f(x) = - 2 x^{3} + 150 x - 3 \).
Problem 3.135easy✓ Every equation proved