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Unformatted text preview: 2. The function f ( x ) = x 2 , x ∈ (-∞ , 0) ∪ (0 , ∞ ) has no local minimum or maximum. 3. The functions f ( x ) = x, x 3 , x 5 have no local minimum or maximum. 4. The functions f ( x ) = sin x, cos x, sec x, csc x have inﬁnitely many local minimums and maximums. The functions f ( x ) = tan x, cot x have no local minimums or maximums. 5. The function f ( x ) = x 4 + x 3-11 x 2-9 x + 18 = ( x-3)( x-1)( x + 2)( x + 3) has two local minimums at x ≈ -2 . 6 and x ≈ 2 . 2 and a local maximum at x ≈ -. 4 . 6. The function f ( x ) = 1 has a local minimum and maximum at any point on the number line. 2...
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