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

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

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 .

i think the correct option is the second option.

its line 2 i just added the rest or else it wouldn't let me answer