Your classmates may have different criteria for their functions, so in your initial post in Brightspace be sure to list the criteria for your function.

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 98E: 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 (z) with the following properties:
• f(x) is decreasing at æ = -6
• f(r) has a local minimum at z = -3
f (x) has a local maximum at z = 3
Your classmates may have different criteria for their functions, so in your initial post in Brightspace be sure to list the criteria for your function.
Hints:
• Use calculus!
• Before specifying a function f (z), first determine requirements for its derivative f' (z). For example, one of the requirements is that f' (-3) = 0.
• If you want to find a function g (z) such that g (-9) = 0 and g (8) = 0, then you could try g(z) = (x+ 9) ( – 8).
• If you have a possible function for f' (z), then use the techniques in Indefinite Integrals this Module to try a possible f (z).
You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before
clicking "How Did I Do?". Notice that the label "f (x) =" is already provided for you.
Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the r-axis go from -6 to 6.
f (x) =
Transcribed Image Text:For this week's discussion, you are asked to generate a continuous and differentiable function f (z) with the following properties: • f(x) is decreasing at æ = -6 • f(r) has a local minimum at z = -3 f (x) has a local maximum at z = 3 Your classmates may have different criteria for their functions, so in your initial post in Brightspace be sure to list the criteria for your function. Hints: • Use calculus! • Before specifying a function f (z), first determine requirements for its derivative f' (z). For example, one of the requirements is that f' (-3) = 0. • If you want to find a function g (z) such that g (-9) = 0 and g (8) = 0, then you could try g(z) = (x+ 9) ( – 8). • If you have a possible function for f' (z), then use the techniques in Indefinite Integrals this Module to try a possible f (z). You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did I Do?". Notice that the label "f (x) =" is already provided for you. Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the r-axis go from -6 to 6. f (x) =
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