For this week's discussion, you are asked to generate a continuous and differentiable function f(x) with the following properties:f(x) is decreasing at x=−5f(x) has a local minimum at x=−3f(x) has a local maximum at x=3 Hints:Use calculus!Before specifying a function f(x), first determine requirements for its derivative f′(x). For example, one of the requirements is that f′(−3)=0 .If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8).If you have a possible function for f′(x), then use the techniques in Indefinite Integrals this Module to try a possible f(x).Please note that the bounds on the x-axis go from -6 to 6.

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Answered: For this week's discussion, you are…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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For this week's discussion, you are asked to generate a continuous and differentiable function f(x) with the following properties:

f(x) is decreasing at x=−5
f(x) has a local minimum at x=−3
f(x) has a local maximum at x=3

Hints:

Use calculus!
Before specifying a function f(x), first determine requirements for its derivative f′(x). For example, one of the requirements is that f′(−3)=0 .
If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8).
If you have a possible function for f′(x), then use the techniques in Indefinite Integrals this Module to try a possible f(x).

Please note that the bounds on the x-axis go from -6 to 6.

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