Here, we had to find theta such that the denominator has the maximum value. Being new to differentiation I basically didn't understand how differentiation solved the purpose:
I basically didnt understand why we differentiated it.
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$\begingroup$ The differential of a cosine function is minus sine and the differential of a sine function is plus cosine. $\endgroup$– FarcherCommented Jun 6, 2016 at 12:31
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$\begingroup$ @Farcher I've made an edit to the question. We had to find theta such that the denominator has the maximum value. I basically didn't understand how differentiation solved the purpose $\endgroup$– oshhhCommented Jun 6, 2016 at 12:36
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2$\begingroup$ At a local maximum of a function, the derivative is zero. The text says they are searching for the maximum, so they set the derivative equal to zero. $\endgroup$– Karsten KoopCommented Jun 6, 2016 at 12:38
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$\begingroup$ Essentially a maths question, but I don't think it's worth migrating, since it's pretty much answered by @KarstenKoop. Expansion: if a function $f(x)$ has a maximum at $x=x_0$, the points immediately either side of $x_0$ have a smaller function value. The derivative of $f(x)$ gives the slope of the tangent to the curve defined by $f(x)$. If the tangent line is ascending, its slope and hence the derivative of $f(x)$ are positive. If the tangent is descending, it's negative. So on one side of a maximum the derivative will be positive, on the other negative. Exactly at the maximum it's zero. $\endgroup$– WouterCommented Jun 9, 2016 at 11:47
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1 Answer
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This is mere math.
In the maximum or minimum points, the slope of the curve is zero. And the differentiation (the derivative) is the slope. So, set the derivative equal to zero, and the solutions are the peaks and valleys on the curve.
http://mathsfirst.massey.ac.nz/Calculus/SignsOfDer/MaxMin.htm
