Question

Find the point on the curve *y*=4*x*+2 closest to
the point (0,4).

(x,y)= (_____,_____)

Answer #1

Find the point on the line 4x + y = 7 that is closest to the
point (−5, 1).
(x,y)=

Find the point on the curve y = sqrt(x) is closest to the point (3,
0) , and find the value of this minimum distance.
Use the Second Derivative Test to show that this value is a
minimum. Show work

In xy-plane, find the point on the curve y^2/x - 9/x = 1
closest to the origin.
a. Name the function f which you are minimizing, and name your
constraint g.
b. Set up a LaGrange multiplier equation, and system of n
equations, n unknowns. Then solve the system of equations.

Find the point on the line 4x+7y-3=0 closest to the point
(-2,-5)

Q1. (a) Find the equation of the tangent to the curve
f(x)=x^2+4x+2 at the point where the gradient is 8.
(b) Find the equation of the normal at this point, where normal
gradient times tangent gradient is -1.

Find the point on the surface (x-3)2 +
(y-2)2 + z2 =1 that is closest to the
origin.

Find the x-value of the point on the line x-y=3 that is closest to
the point (-2,0).

1.
Find the point on the line y = x − 6 that is closest to the origin
2. Find the rate of change ds/dt of the function S= x^2+y^2
when x=9, y=15, dx/dt=2, dy/dt=-1

Find the exact length of the curve y=(x^3)/3 + 1/(4x) for
2≤x≤3
Conslder the curve deflned by x=t+1 and y=t^2. Find the
corresponding rectangular equation. Produce two graphs: one using
the rectangular equation and one using the parametric equations.
What are the differnce's between the graphs?
Please show work.

Find the point on the line 4x+2y−4=0 which is closest to the
point (1,3).

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