Applied Max And Min (Optimization) Calculus Worksheet With Answers Page 28
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30 X
h
5
5
5
Area of a trapezoid = h( a + b)
where a and b are the parallel sides and h is the
perpendicular distance between them
2
We can use right triangle trig to find h and X in terms of θ.
X
5
h
= cos θ
= sinθ
h
5
5
h = 5sinθ
x = 5cosθ
X
So the Area of a trapezoid = h( a + b)
2
= 5sin θ( 5 + 5 + 2*5cosθ)
2
A
= 25sinθ + 25sinθcosθ
use product rule to find the
derivative of this term
A'(x ) is ugly !!!
A'(x) = 25sin2θ + 25cos 2θ+ 25cosθ
Use a calculator to solve for the zeros and do the sign line.
Title: Oct 133:45 PM (28 of 30)
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