Find the dimensions of the rectangle of largest area that

Cabiolab 2021-08-14 Answered
Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.)
y=6x2
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Expert Answer

hosentak
Answered 2021-08-15 Author has 100 answers
Area of the rectangle is A=xySubstitue y=6x2in the formula of the area.A=x(6x2)
=6xx3Diferentiate area with respect to x and equate to 0.A=ddx(6xx3)
=63x2
63x2=0
3x2=6
x=±2
Substitutex=±2  y=6x2to get value of height,y=6x2
=6(2)2
=4Hence. the dimensions of rectangle are,22×4.
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