The table below shows experimental values for z at particular values of x and y.

Question

The table below shows experimental values for z at particular values of x and y. The values of x are in the top margin and the values of y are in the left margin. a. Estimate partial differential z/partial differential x, partial differential z/partial differential y, partial differential^2z/partial differential x^2, partial differential^2z/partial differential y^2, and partial differential^2z/partial differential x partial differential y at (60, 300). b. Estimate the maximum rate of change in z at (60, 300). C. Estimate the rate of change in z at (60, 300) in the direction .

Explanation / Answer

a)

z/x =[5495-2116]/(80-40)=84.475

z/y =[4161-3027]/(350-250)=11.34

z2/x2=[((5495-3578)/(80-60))-((3578-2116)/(60-40))]/(80-40)=91/160=0.56875

z2/y2=[((4161-3578)/(350-300))-((3578-3027)/(300-250))]/(350-250)=4/625=0.0064

z2/xy =[((6392-4650)/(350-250))-((2461-1790)/(350-250))]/(80-40)=1071/4000=0.26775

b)

maximum rate of change of z at (60,300)=[84.4752+11.342]

maximum rate of change of z at (60,300)=85.233

c)

rate of change in z at (60,300) in direction <1,4> is =<84.475,11.34>.<1,4>/[12+42]

rate of change in z at (60,300) in direction <1,4> is =[(84.475*1)+(11.34*4)]/17

rate of change in z at (60,300) in direction <1,4> is =31.49

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.