For this week's discussion, you are asked to generate a continuous and differentiable function f(z) with the following properties: . f(z) is decreasing at z =-6 . f(z) has a local minimum at z = -2 • f(z) has a local maximum at z = 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(z), first determine requirements for its derivative f' (z). For example, one of the requirements is that f'(-2) = 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)= (2+9)(z-8). • If you have a possible function for f (2), 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(z) =" 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 z-axis go from -6 to 6. It is recommended that you put a multiplication symbol between variables or between a variable and (should you use it). Example: Write sin (-2)instead of sin (Z). f(z) =
For this week's discussion, you are asked to generate a continuous and differentiable function f(z) with the following properties: . f(z) is decreasing at z =-6 . f(z) has a local minimum at z = -2 • f(z) has a local maximum at z = 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(z), first determine requirements for its derivative f' (z). For example, one of the requirements is that f'(-2) = 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)= (2+9)(z-8). • If you have a possible function for f (2), 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(z) =" 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 z-axis go from -6 to 6. It is recommended that you put a multiplication symbol between variables or between a variable and (should you use it). Example: Write sin (-2)instead of sin (Z). f(z) =
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.7: A Library Of Parent Functions
Problem 47E
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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(z) is decreasing at z = -6
f(x) has a local minimum at = -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(z), first determine requirements for its derivative f' (z). For example, one
of the requirements is that f'(-2) = 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) (z - 8).
• If you have a possible function for f¹ (z), 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 z-axis go from -6 to 6. It is recommended that you put a multiplication symbol between
variables or between a variable and π (should you use it). Example: Write sin (-2)instead of sin (TZ).
f(x) =
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