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QUESTION

CALCULUS

a)Find the exact location of all the relative and absolute extrema of the function.

g has  ---Select--- a relative minimum a relative maximum an absolute minimum an absolute maximum no extremum

at (t, y) = 

g has  ---Select--- a relative minimum a relative maximum an absolute minimum an

absolute maximum no extremum at 

g has  ---Select--- a relative minimum a relative maximum an absolute minimum an absolute maximum no extremum at 

(t, y) = 

Find the indicated derivative using implicit differentiation.

Find the indicated derivative using implicit differentiation

xey − yex = 5; 

Find the exact location of all the relative and absolute extrema of the function. HINT

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ANSWER

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*********** *** ********* derivative ***** implicit *************** **** **** Example 1]x2y−y2=8;dy ************* * ******* ** = ******* *** -8) * dy( y2)dx ******* ****** *** = *** ******** dx =2x **** + ********* = 2y y’(x) =2x y(x) * y’(x)x2 *** ******* =0  ********* *** y’(x)=- ** ****** *** ******* ***** *** **** ******** ******* 2y **** * * ** *********** 2y) =- ****** **** * - ** * **** 2y) Find the indicated derivative ***** ******** *************** **** **** Example ************************** ******* * dy(5)dx ******* * function ** * ** *************** ********** = ******* ********* product **** *** ***** *************** ) ** ********* as **************** ******* ** ***** 1v= ey(x) * ************** ********* ) * ***** * xy’(x)ey(x) ******** ********** ********** +y(x)ex ************** ** ******** * **** ********* we get ey(x) * ************* - y’(x)ex ******* ******* y(x) ** *** ******* =y’ ****** *** ******** y’ex **** =0  ******** y’ex + - ** * ************* * ex) = * *** * **** **** * ex) * * ********* y’ **** * yex) * *********** *** exact ******** ** *** the ******** *** absolute ******* ** the ******** **** **** ******* ****** *** + ********* * t3 – *** * * ** t(t2 – ** * *** ******** ** (t-1)2 =0 ***** ** ** ************* ***** ******** ************** =0 and **** *** ** ** *** t= againWe **** **** *** extrema the relative minima ** this **** ** critical point ******* ***** * **** = 1/12 **** Relative ****** ** ********** ****** ******* *************** ***** ** * the ******** extrema ** ***** (1083)ie ******** minima ** ***** ************* this ***** *** no ***** ******** point ** this ****** point (1083) remains ** ** *** ******** ****** the ***** *** neither ***** nor global maxima   ghas---Select---a ******** ******** ******** ********* ******** minimuman ******** ********* ************* *** * ******** ****** ****** ********** has ** ************ the ***** location ** *** the ******** *** ******** extrema ** *** ******** **** **** ******* ****** *********** ****** ***** ***** **** * et–t g’(t) * ** -1=0 ** **** 1 *** ** ** ** 0critical ***** is *** ******** ******* ** point ****** ******** ****** ** ***** ************ ****** ** ***** (1 ************ minima ** ***** *** ************************ ******** ******** ******** ********* ******** ********* ******** maximumno ************** **** has * ******** minimum (ty) ************************** relative minimuma ******** ********* absolute ********* absolute ********* **************** ************************** ******** ******** relative ********* ******** minimuman ******** ********* ************** ***** seems *** *** ***** * popdown **** kindly make use the ******* in *** ** ****** *** ************* ******** to **** ** ****

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