Sun K.

asked • 05/02/13

Find the maximal value of f(x, y)?

Find the maximal value of f(x, y)=3y+4x on the circle x^2+y^2=1.

Sun K.

But how did you find the slope, which is -4/3? And how did you find (4a, 3a)?

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05/02/13

Robert J.

3y+4x = c

The slope of the line is -4/3

At the point of tangency on the circle, the slope must be 3/4 such that the radius is perpendicular to the tangent line. So, we can assume the point at (4a, 3a).

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05/02/13

2 Answers By Expert Tutors

By:

Robert J. answered • 05/02/13

Tutor
4.6 (13)

Certified High School AP Calculus and Physics Teacher

Grigori S. answered • 05/02/13

Tutor
New to Wyzant

Certified Physics and Math Teacher G.S.

Hossein F.

Grigori, You have an error when differentiating with respect to x:

f'=4-3x/sqrt(1-x2)

Using this and following through with your solution you will get max value of f(x,y) on the circle is 5.

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05/03/13

Grigori S.

You are right. This was an accident. I was doing part of my calculations mentally and forgot to cancel two 2-s, in the numerator and denominator. If you solve my equations after these corrections you will come with x = 4/5 and y = 3/5

and the maximum will be  f(x) = 5 as found by Robert. He did very good job and was more accurate with numerical calculations.

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05/03/13

Grigori S.

You are right. This was an accident. I was doing part of my calculations mentally and forgot to cancel two 2-s, in the numerator and denominator. If you solve my equations after these corrections you will come with x = 4/5 and y = 3/5

and the maximum will be  f(x) = 5 as found by Robert. He did very good job and was more accurate with numerical calculations.

Report

05/03/13

Grigori S.

You are right. This was an accident. I was doing part of my calculations mentally and forgot to cancel two 2-s, in the numerator and denominator. If you solve my equations after these corrections you will come with x = 4/5 and y = 3/5

and the maximum will be  f(x) = 5 as found by Robert. He did very good job and was more accurate with numerical calculations.

Report

05/03/13

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