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<oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'>
<dc:creator>Dumitru, B.</dc:creator>
<dc:date>2010</dc:date>
<dc:description xml:lang='en'><p>According to the curriculum, in mathematics the differential calculus is studied in the 9th grade, sciences. The main mathematical concepts introduced are: the increment of argument, the increment of function, the average speed and the instantaneous speed of the function of variation, the derivative of a function at a point, the derivative of a function on a closed interval, chord, tangent, the gradient of a chord and the gradient of the tangent, the equation of the tangent at the given point, derivable functions, lateral derivates, the differential of a function. The definition of the derivative of the function y=f(x) at a given point is introduced by lim of the ratio of the increment of the function to the increment of the argument, while the increment of the argument approaches 0. f x        )()( lim)( 00 0 0 The concepts of lateral derivatives are introduced in the same way: If there takes place the equality       000 xfxfxf ds     then it is said that the function f is derivable at the point x=x. The differential of a function is defined as a function of a variable dx, if we have the differentiable function f:D&rarr;R, y =f(x), then the function df(x)=f&#39;(x0)dx, where f(x0) is the derivative of the function at the point x0, dx is the differential of the argument, is called the differential of a function f in x = x0. The applicability of the differential in the approximate calculus: 1. the monotony of function; 2. the extremes of a function; 3. the maximum and minimum values of a function at the given interval; 4. tracing the graphs of functions; 5. solving problems of extremes; 6. modeling technical and economical problems.</p></dc:description>
<dc:source>Totalizarea activităţii de cercetare a cadrelor didactice (Vol.2) 19-58</dc:source>
<dc:title>Didactica calculului diferenţial &icirc;n cursul liceal de matematică</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
</oai_dc:dc>