solve d e f Question 1 The little details of Fermat's theorem, the first derivative test, and the second derivative test areimportant. This problem addresses some common misconceptions about some of these details.(a) Give an example of a function f such that f(3) is a local maximum and f"(3) = 0.(b) Give an example of a function f such that f"(3) is undefined but f(3) is a local minimum.(c) Give an example of a function f such that f"(3)0 but f is concave up for all x.(d) Give an example of a function f such that f(3) is a local maximum and f'(3) is undefined.(e) Give an example of a function f such that f'(3) is undefined, but f(3) is neither a local minimumnor local maximum.(f) Give an example of a function f that is increasing for all x, but f'(3) = 0.

problem: (d) Give an example of a function f such that f3 is a local maximum and f'3 is undefined.…

Answered: The little details of Fermat's theorem,…

The little details of Fermat's theorem, the first derivative test, and the second derivative test are important. This problem addresses some common misconceptions about some of these details.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
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On the topic of maxima and minima. Question attached to image.
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