Explanation Consider the given statement: If the partial derivatives with respect to x and y at some point are both 0, the tangent plane to the function at that point is horizontal. The given statement is true. For 3D graphs of functions, the partial derivatives with respect to x , y and z axes. For example, if the function is f ( x , y , z ) and partial derivatives with respect to x , y and z are f x ( x 1 , y 1 , z 1 ) , f y ( x 1 , y 1 , z 1 ) and f z ( x 1 , y 1 , z 1 ) respectively, then f x ( x 1 , y 1 , z 1 ) = tan θ 1

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.CR, Problem 4CR

To determine

The given statement is true or not and give the reason.

Statement: “If the partial derivatives with respect to x and y at some point are both 0, the tangent plane to the function at that point is horizontal”.

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Chapter 9.CR, Problem 3CR

Chapter 9.CR, Problem 5CR

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Chapter 9 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

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The given statement is true or not and give the reason. Statement: “If the partial derivatives with respect to x and y at some point are both 0, the tangent plane to the function at that point is horizontal”.

Solution Summary: The author explains that if the partial derivatives with respect to x and y at some point are both 0, the tangent plane to the function at that point is horizontal.

The given statement is true or not and give the reason. Statement: “If the partial derivatives with respect to x and y at some point are both 0, the tangent plane to the function at that point is horizontal”.

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Chapter 9 Solutions

The given statement is true or not and give the reason.

Statement: “If the partial derivatives with respect to x and y at some point are both 0, the tangent plane to the function at that point is horizontal”.