Optimisation of function

Limits, differentiation, related rates, integration, trig integrals, etc.
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Joined: Mon Apr 02, 2012 12:06 pm

Optimisation of function

Postby lamlon » Mon Apr 02, 2012 12:16 pm

A metal channel is formed by turning up the sides of width x of a rectangular sheet of metal through an angle theta. If the sheet is 200mm wide, determine the values of x and theta for which the cross-section of the channel will be a maximum. The answer from the book give x = 200/3 and theta = pi/3 but I have no idea how to go about solving this, any help would be appreciated thanks.

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Joined: Sun Dec 14, 2008 11:07 pm

Re: Optimisation of function

Postby nona.m.nona » Mon Apr 02, 2012 1:10 pm

To start, draw the cross-sectional view. The sheet is 200 units wide, so label the turned-up sides with "x", the base with "200 - 2x", and the corners with "theta". If you draw a line across the top, what expression would stand for the area within?

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