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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 = –6 f (x) has a local minimum at x = -2 f (x) has a local maximum at x = 2 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 (x), first determine requirements for its derivative f' (x). For example, one of the requirements is that f'(-2) = 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). 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 x-axis go from -6 to 6. f (x) =

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 = –6 f (x) has a local minimum at x = -2 f (x) has a local maximum at x = 2 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 (x), first determine requirements for its derivative f' (x). For example, one of the requirements is that f'(-2) = 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). 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 x-axis go from -6 to 6. f (x) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 = –6 f (x) has a local minimum at x = -2 f (x) has a local maximum at x = 2 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 (x), first determine requirements for its derivative f' (x). For example, one of the requirements is that f'(-2) = 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). 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 x-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 (x) with the following properties: • f (x) is decreasing at x = –6 f (x) has a local minimum at x = -2 f (x) has a local maximum at x = 2 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 (x), first determine requirements for its derivative f' (x). For example, one of the requirements is that f'(-2) = 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). 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 x-axis go from -6 to 6. f (x) =
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