Math CentralQuandaries & Queries


Question from Guido:

This is a calculus 1 question. I understand the question but the different variables in the function make it hard to find D prime.
I believe to find the maximum deflection, I must find D prime and then set D prime to zero to find the critical numbers.
I am stuck at this point.


The deflection D of a particular beam of length L is

$D = 2x^4 - 5Lx^3 + 3L^2x^2$

where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection.

Hi Guido,

You need to treat $L,$ the length of the beam as a constant rather than a variable. What you will end up with is an expression that gives the value of $x$ that yields the maximum deflection for any beam length $L.$

For the differentiation I want to look at a similar expression $f(x) = k x^3 - 7 x^2 + k^3 x - 4k.$ Treating $k$ as a constant and $x$ as the variable I get

\[f^{\prime}(x) = 3k x^2 - 14 x + k^3\]

Try the problem now and write back if you need more assistance,

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