To find the extreme values of a function f(x,y) on a curve x= x(t), y = y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. As in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. Find the absolute maximum and minimum values of the following function on the given curves. Use the parametric equations x = 2 cost, y= 2 sin t. Functions: Curves: i) The semicircle x + y? = 4, y20 ii) The quarter circle x? +y? = 4, x20, y 20 а. f(x.y) = x+y b. g(x,y) = xy c. h(x.y) = 2x2+ y? a. On the semicircle, the absolute maximum is f=at t=D. (Type exact answers, using z as needed. Use a comma separate answers as needed.)

To find the extreme values of a function f(x,y) on a curve x= x(t), y = y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. As in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. Find the absolute maximum and minimum values of the following function on the given curves. Use the parametric equations x = 2 cost, y= 2 sin t. Functions: Curves: i) The semicircle x + y? = 4, y20 ii) The quarter circle x? +y? = 4, x20, y 20 а. f(x.y) = x+y b. g(x,y) = xy c. h(x.y) = 2x2+ y? a. On the semicircle, the absolute maximum is f=at t=D. (Type exact answers, using z as needed. Use a comma separate answers as needed.)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

= x(t), y = y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. As in any other single-variable case, the extreme values of f are then found
To find the extreme values of a function f(x,y) on a curve x=:
among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. Find the absolute maximum and minimum values of the following function on the given curves. Use the parametric
equations x =2 cos t, y = 2 sin t.
Functions:
Curves:
i) The semicircle x? + y? = 4, y 2 0
ii) The quarter circle x² + y = 4, x 2 0, y 20
а. f(х,у) — х+у
b. g(x,у) 3 ху
c. h(x,y) =
2x? + y?
a. On the semicircle, the absolute maximum is f=
at t =
(Type exact answers, using n as needed. Use a comma to separate answers as needed.)

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