Overview
The original 24 m edge length x of a cube decreases at the rate of 44
m/min.
a. When xequals=55
m, at what rate does the cube's surface area change?
b. When xequals=55
m, at what rate does the cube's volume change?
a. nbspa.
When xequals=55
m, the surface area is changing at a rate of
nothing
m squaredm2/min.
(Type an integer or a decimal. Do not round.)
Let x and y be differentiable functions of t, and let sequals=StartRoot 3 x squared plus 3 y squared EndRoot3x2+3y2
be a function of x and y. Answer the following questions.
a. How is StartFraction ds Over dt EndFractiondsdt
related to
StartFraction dx Over dt EndFractiondxdt
if y is constant?
StartFraction ds Over dt EndFractiondsdtequals=left parenthesis nothing right parenthesis StartFraction dx Over dt EndFraction3x3x2+3y2dxdt
b. How is StartFraction ds Over dt EndFractiondsdt
related to
StartFraction dx Over dt EndFractiondxdt
and
StartFraction dy Over dt EndFractiondydt
if neither x nor y is constant?
StartFraction ds Over dt EndFractiondsdtequals=left parenthesis nothing right parenthesis StartFraction dx Over dt EndFraction plus left parenthesis nothing right parenthesis StartFraction dy Over dt EndFractiondxdt+dydt
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