Answered: For the slope field shown, which could…

For the slope field shown, which could be a family of anti-derivatives? y -6.28 6.28 O y = – cos x + C O y =x + C o y = sin x + C O y =x + C /// //// /// // /// // / // // // /// ///

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 54CR

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Question

Please explain how to solve. Thank you!

For the slope field shown, which could be a family of anti-derivatives?
y
-6.28
6.28
оу%3 — соS х + C
|
O y = x + C
o y= sin x + C
O y = x + C
///
/ { /// //
///
// ///
///
/////
////
/////

Expert Solution

Step 1

Given slop field is

Now we check all options one by one.

option 1:

Given

$y = - \cos (x) + C$

Differentiating, we get

$y' = c o x$

So, slop field for above is

option 2:

Given

$y = x^{2} + c \Rightarrow y' = 2 x$

So, slop field is

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