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    <p>The function </p> <pre><code>def fixedPoint (f: Double =&gt; Double)(firstGuess: Double):Double </code></pre> <p>is a function definition which takes two arguments:</p> <ol> <li>a function "f" which takes a parameter of type <code>Double</code> which returns a <code>Double</code> and</li> <li>a <code>Double</code> value named "firstGuess"</li> </ol> <p>and returns a <code>Double</code>. The separation of the single parameters into their own parenthesis groups allows the function to be used in currying:</p> <pre><code>def mySqrtCalc(x:Double)(firstGuess:Double):Double = {...} val mySqrtFunc = mySqrtCalc(2.0) _ val v = mySqrtFunc(1) // parameter firstGuess is set to 1 </code></pre> <p>Beside the ability for currying, this is equivalent to the uncurried version</p> <pre><code>def fixedPoint (f: Double =&gt; Double,firstGuess: Double):Double </code></pre> <p>which might look more familiar to you.</p> <p>The result of the <code>calculateAverate</code> is a Double because you add up the result of applying the passed function f to x with x which gives you a <code>Double</code> because f is a function <code>Double =&gt; Double</code>.</p> <p>You use <code>calculateAverate</code> method in a curried way in your <code>myNewSquareRoot</code> method body, by giving only the first of both parameters in first place and omitting the second one, which is taken from the from the outer <code>fixedPoint</code> method. Omitting the second parameter of <code>calculateAverate</code> gives you a method <code>Double=&gt;Double</code> as it is required by the <code>fixedPoint</code> method. </p> <p>You might insert some <code>println(s"&lt;methodname&gt; value=$value")</code> to observe the execution flow and understand the method call order.</p>
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    1. COThanks for such a great explanation. I think in the example you provided you missed one part def mySqrtCalc(x:Double)(firstGuess: Double):Double = {...}.. right?
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    2. CORight, thanks - edited my answer accordingly
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