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Annotation of loncom/homework/templates/extreme.problem, revision 1.1

1.1     ! www         1: <problem>
        !             2:     <parameter name="ordered" type="string_yesno" description="Show Parts One-at-a-Time" default="yes" />
        !             3: 
        !             4: <script type="loncapa/perl">
        !             5: $location=&random(4,10,1);
        !             6: $example="(x-$location)^2";
        !             7: if (&random(0,1,1)) {
        !             8:    $text='minimum';
        !             9:    $factor=1;
        !            10: } else {
        !            11:    $text='maximum';
        !            12:    $factor=-1;
        !            13:    $example='-'.$example;
        !            14: }
        !            15: 
        !            16: # Get user input, run through function that adds "*" to 3x, etc
        !            17: $userfunction=&implicit_multiplication(&submission(1,11));
        !            18: if ($userfunction) {
        !            19: # Determine value at extreme point
        !            20:    $extremevalue=&cas('maxima',"float(at($userfunction,x=$location))");
        !            21:    if ($extremevalue=~/^(error|incorrect)/i) {
        !            22: # cas could not evaluate the function
        !            23:       $userfunction='0';
        !            24:       $extremevalue=0;
        !            25:       $remark='Your function could not be evaluated.';
        !            26:    } else {
        !            27:       $remark='Your function is plotted.';
        !            28:       $example=$userfunction;
        !            29:    }
        !            30: } else {
        !            31:    $userfunction='0';
        !            32:    $extremevalue=0;
        !            33:    $remark='';
        !            34: }
        !            35: # Plot boundaries
        !            36: $minx=$location-5;
        !            37: $maxx=$location+5;
        !            38: $miny=$extremevalue-5;
        !            39: $maxy=$extremevalue+5;
        !            40: @args=($location,$factor);
        !            41: </script>
        !            42: 
        !            43: <part id="1">
        !            44: <gnuplot width="400" solid="0" plotcolor="monochrome" gridlayer="off" bmargin="default" font="9" alttag="Plot" bgcolor="xffffff" texfont="22" transparent="off" plottype="Cartesian" rmargin="default" gridtype="Cartesian" minor_ticscale="0.5" fontface="sans-serif" grid="on" align="middle" texwidth="93" height="300" border="on" samples="100" fgcolor="x000000" major_ticscale="1" tmargin="default" lmargin="default" fillstyle="empty">
        !            45:     <curve 
        !            46:          linestyle="lines"
        !            47:          color="x000000"
        !            48:          pointtype="1"
        !            49:          linetype="solid"
        !            50:          linewidth="1"
        !            51:          name=""
        !            52:          limit="closed"
        !            53:          pointsize="1" >
        !            54:         <function>$userfunction</function>
        !            55:         
        !            56:         
        !            57:     </curve>
        !            58:     <axis yzero="off" xformat="on" xmin="$minx" yformat="on" color="x000000" xmax="$maxx" xzero="off" ymax="$maxy" ymin="$miny" />
        !            59:     
        !            60: </gnuplot>
        !            61: 
        !            62: <startouttext />
        !            63: <p>$remark</p>
        !            64: Give a differentiable real function <m>$f(x)$</m> that has a $text at <m eval="on">$x=$location$</m>.<br />
        !            65: <m>$f(x)=$</m>
        !            66: <endouttext />
        !            67: 
        !            68: <mathresponse answerdisplay="$example" cas="maxima" args="@args" id="11">
        !            69:     <answer>y(x):=RESPONSE[1];
        !            70: hasextreme:is(at(diff(y(x),x,1),x=LONCAPALIST[1])=0);
        !            71: isrightkind:false;
        !            72: k:0;
        !            73: s:0;
        !            74: if hasextreme then for i:2 while s=0 do (s:at(diff(y(x),x,i),x=LONCAPALIST[1]),k:i);
        !            75: if evenp(k) and is(LONCAPALIST[2]*s>0) then isrightkind:true;
        !            76: hasextreme and isrightkind;</answer>
        !            77:     <textline readonly="no" size="50" />
        !            78: </mathresponse>
        !            79: </part>
        !            80: <part id="2">
        !            81: <script type="loncapa/perl">$value=&cas('maxima',"float(at($example,x=$location))");</script>
        !            82: <startouttext />
        !            83: What is the value of your function at this $text?
        !            84: <endouttext />
        !            85: <numericalresponse answer="$value">
        !            86: <responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance" />
        !            87: 
        !            88:     <textline readonly="no" />
        !            89:     
        !            90: </numericalresponse>
        !            91: </part>
        !            92: </problem>