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        <TITLE>Calculus I Applications</TITLE>
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        <h1>Applications and Meaning</h1>
        <h3>This page contains a quick list of main topics and what they're used for</h3>
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	<h3> 1.) First derivative </h3>
	<p>
	The derivative of a function represents the slope of a tangent line at a point. Even simpler, the derivative of a function at some x, is the rate of change of that function at that x.  
	<p>	
	Three Rules for f'(x):
	<p>
	First Rule: f'(x) > 0 when f(x) is increasing.
	<p>
	Second Rule: f'(x) < 0 when f(x) is decreasing.
	<p>
	Third Rule: f'(x) = 0 when f(x) has a horizontal tangent. (Slope of 0.)
	<p>
	<hr>
	<h3> 2.) Second derivative </h3>
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	The second derivative of a function represents the concavity of the graph at a x. 
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	Three Rules for f''(x):
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	First Rule: f''(x) > 0 when f(x) is concave up.
	<P>
	Second Rule: f''(x) < 0 when f(x) is concave down.
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	Third rule: A point of inflection is a location where concavity changes. (f''(0) does not imply point of inflection always)
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	<h3> 3.) Trig(Unit circle seen at bottom) </h3>
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	One of the most important things to learn is SOHCAHTOA
	<p>
	SOH : sin = <sup> Opposite</sup> / <sub> Hypotenuse</sub>
	<p>
	CAH : cos = <sup> Adjacent</sup> / <sub> Hypotenuse</sub>
	<p>
	SOH : Tan = <sup> Opposite</sup> / <sub> Adjacent</sub>
	<p>
	Having these Double angle identities will be extremely beneficial when trying to simplify problems:
	<p>
	sin<sup>2</sup>(x) + cos<sup>2</sup>(x) = 1
	<p>
	sin<sup>2</sup>(x) = <sup>1</sup>/<sub>2</sub>(1-cos(2x))
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	cos<sup>2</sup>(x) = <sup>1</sup>/<sub>2</sub>(1+cos(2x))
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	tan<sup>2</sup>(x) = sec<sup>2</sup>(x)-1
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	cot<sup>2</sup>(x) = csc<sup>2</sup>(x)-1
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	sin(x)cos(x) = <sup>1</sup>/<sub>2</sub>sin(2x)
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