Find the maximum and minimum values attained by the function f along t

aspifsGak5u 2021-12-14 Answered
Find the maximum and minimum values attained by the function f along the path c(t).
(a)f(x,y)=xy;c(t)=(cos(t),sin(t));0t2π
maximum value__________
minimum value__________
(b) f(x,y)=x2+y2;c(t)=(cos(t),8sin(t));0t2π
maximum value__________
minimum value__________
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Paineow
Answered 2021-12-15 Author has 30 answers
Srep 1
(a)
Given that, f=(x,y)=xy;c(t)=(cost,sint);0t2π.
c(t)=xj^+yj^
=(cost)j^+(sint)j^
f(x,y)=cost×sin
=sin(2t)2
(sin2α=2sinαcosα)
It is known that, the range of the sine functions is -1 to 1.
1sin(2t)1
12sin(2t)212
12f(x,y)12
Thus, the function has the maximum value 12 and minimum vaiue 12.

We have step-by-step solutions for your answer!

ramirezhereva
Answered 2021-12-16 Author has 28 answers

Step 2
(b)
Given that, f(x,y)=x2+y2;c(t)=(cost,8sint);0t2π.
c(t)=xj^+yj^
=(cost)j^+(8sint)j^
f(x,y)=(cost)2+(8sint)2
=cos2t+64sin2=1sin2t+64sin2=1+63sin2
It is known that, the range of the sine function is -1 to 1.
0sin2t1
063sin2t63
11+63sin2t64
1f(x,y)64
Thus, the function has the maximum value 64 and minimum value 1.

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-05-14
Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)
b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)
c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)
d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)
e) The coordinates of the point of inflection. (x, y)=
asked 2022-02-01
What is the polar form of (-200, 10)?
asked 2021-06-03
Let P(x)=F(x)G(x) and Q(x)=F(x)G(x), where F and G are the functions whose graphs are shown.
a) Find P(2)
b) Find Q(7)
asked 2021-08-21
Change from rectangular to spherical coordinates. (Let ρ0, 0θ2π, and 0ϕπ.)
a) (0, 8, 0)(ρ,θ,ϕ)=?
b) (1, 1, 2)(ρ,θ,ϕ)=?
asked 2021-09-09

Find the point(s) of intersection of the following two parametric curves, by first eliminating the parameter, then solving the system of equations.
x=t+5,y=t2andx=116t,y=t
a. (25, 400)
b. (1, 16)
c. (400, 16)
d. A and B
e. A and C

asked 2021-12-04
Represent the line segment from P(2, 3, 8), Q(5, 1, 2) by a vector-valued function and by a set of parametric equations.
asked 2021-11-20
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x=1+2t, y=t3t, z=t3+t; (3,0,2)

New questions