Answer:
2/5
Step-by-step explanation:
Answer:
Point Critical point
Q (2,0) local minimum
R (-2,1) Saddle
S (2,-1) local maximum
T ( -2,-1) Saddle
O ( -2,0) Saddle
Step-by-step explanation: INCOMPLETE ANSWER INFORMATION ABOUT THE POINTS ARE RARE
f(x,y) = x³ +y⁴ - 6x -2y² +3
df/dx = f´(x) = 3x² -6x
df/dxdx = f´´(xx) = 6x
df/dy = f´(y) = -4y
df/dydy = 4
df/dydx = df/dxdy = 0
df/dydy = f´´(yy)
D = [ df/dxdx *df/dydy] - [df/dydx]²
D = (6x)*4 - 0
D = 6*2*4 D > 0 and the second derivative on x is 6*2 = 12
so D > 0 and df/dxdx >0 there is a local minimum in P
Q(2,1)
D = (6*2)*4 D>0 and second derivative on x is 6*2
The same condition there is a minimum in Q
R ( -2,1)
D = 6*(-2)*4 = -48 D< 0 there is a saddle point in R
S (2,-1)
D = 6*2*4 = 48 D > 0 and df/dxdx = 6*-1 = -6
There is a maximum in S
T ( -2,-1)
D = 6*(-2)*(4) = -48 D<0 there is a saddle point in T
O ( -2,0)
D = 6*(-2)*4 = -48 D<0 there is a saddle point in O
Answer:
x = 3
y = 3/2
Step-by-step explanation:
look at the hangers to form an equation:
x + x + x + 3 + 3 + 3 = x + x + y + y + y + y
simplify
3x + 3 = 2x + 4y
x + 3 = 4y
x = 4y - 3
you also know that
x + x = y + y + y + y
2x = 4y
substitute x = 4y - 3 into this equation ^
2x = 4y
2(4y - 3) = 4y
8y - 6 = 4y
4y = 6
y = 6/4
y = 3/2
2x = 4y
2x = 12/2
2x = 6
x = 3
Answer:
graph it
Step-by-step explanation:
Answer:
2t
Step-by-step explanation:
