题目

MATH136-12P-IO-202510-I-81X M04: Midterm Exam Review Quiz

多项填空题

State when the function is increasing and decreasing using interval notation. Use inf for ∞\infty. Increasing: [Fill in the blank], Decreasing: [Fill in the blank],

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思路分析

To determine where a function is increasing or decreasing, we analyze the sign of its derivative. Specifically, a function is increasing on intervals where f'(x) > 0 and decreasing where f'(x) < 0. The question provides four candidate interval endpoints for the two blanks and asks us to reason about them. Option set for the increasing interval: (0, ∞) or [0, ∞) are the two kinds of answers given in the list if we consider the first placeholder to be one of the choices. If we assume the derivative is positive for all x > 0 but not at x = 0, then the natural open interval (0, ∞) reflects an interval where the function is strictly ......Login to view full explanation

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类似问题

Given a function whose graph is shown below, under which interval/s is the graph increasing? A. ( − 3 , − 1 ) ∪ ( 2 , 4 ) B. ( − 1 , + ∞ ) C. ( − 3 , 1 ) D. ( − ∞ , − 3 ) ∪ ( − 1 , 2 ) ∪ ( 4 , + ∞ )

For 𝑓 and 𝑔 real valued functions defined for all real numbers, ( 𝑔 ∘ 𝑓 ) ( 𝑥 ) = 𝑔 ( 𝑓 ( 𝑥 ) ) or all 𝑥 . Which of the following is (are) true? I. If 𝑓 is increasing and 𝑔 is increasing, then 𝑔 ∘ 𝑓 is increasing. II. If 𝑓 is increasing and 𝑔 is decreasing, then 𝑔 ∘ 𝑓 is decreasing. III. If 𝑓 is decreasing and 𝑔 is increasing, then 𝑔 ∘ 𝑓 is decreasing.