Sun K.

# 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:

Tutor
4.6 (13)

Certified High School AP Calculus and Physics Teacher

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.

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

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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