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gshreya2005
06.10.2019 •
Mathematics
Find the critical points of the following function. use the second derivative test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. if the second derivative test is inconclusive, determine the behavior of the function at the critical points. f(x,y)=−8x2+6y2−14
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Ответ:
Answer with Step-by-step explanation:
We are given that a function
We have to find the critical points and find the function has local maximum, local minimum, or saddle point using second derivative test.
Differentiate w.r.t x
Differentiate function w.r.t y
To find the critical point
Substitute![f_x=0,f_y=0](/tpl/images/0292/9748/487bc.png)
The critical point is (0,0).
Value of D at critical point (a,b)
Substitute the values then we get
Therefore, the function has saddle point at (0,0) because when D < 0 the f(x,y) has saddle point at critical point
.
Ответ: