Consider the function f(x,y)=e8xx28yy2. Find and classify all critical points of

Question

Consider the function f(x,y)=e8xx28yy2. Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank.

fx=

fy=

fxx=

fxy=

fyy=

The critical point with the smallest x-coordinate is (_,_ ) Classification:________ (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest x-coordinate is (____,____ ) Classification:________ (local minimum, local maximum, saddle point, cannot be determined)

Explanation / Answer

f(x,y)=e8x-x2-8y-y2

fx=8e8x-2x

fy=-8-2y

fxx=64e8x-2

fyy=-2

for critical point,

fx   and fy   should must be 0.

so,

8e8x-2x=0 and

-8-2y=0

y=-4

but there is no points for the x which satisfies the given condition.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects