A rectangle has dimensions 0.7x and 5 - 3x. What value of x gives the maximum area and what is the maximum area?
2 Answers
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Explanation:
Given dimensions of the rectangle are:
Area of the rectangle
Area of the rectangle
To maximize the area the first derivative is to be set equal to
or
or
To confirm that it is a maximum we need to evaluate second derivative at the obtained value of
Second derivative
Maximum Area
Maximum area =
(
Explanation:
Let the area be
From the question the area is:
Rate of change in
Using calculus: shortcut method
Rate of change is zero at maximum area
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
to find the fractional solution:
so
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus the exact area is
The approximate area is