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
So for example we have
1/2 divided by 1/6
What we will do it’s
Leave the first one As it is
Turn the second fraction (the one you want to divide by) upside down
The change the divide to multiply
Multiply the first fraction by that reciprocal
Simplify the fraction (if needed)
So it’s will be like this
1/2 x 6/1 = 6/2
Simplify it
6/2 =3
I hope it’s will help u ✨
Christopher needs to create so that his time spent will be the same as his current time, the equation could be: 2.4x = 1.2x + 15
(125^2x)(5x) = 25^3
(15625x)(5x)=15625
<span>78125x=15625
</span>x=5
Hope I helped ;D
8x-9y=11
First you move the 8x because you have to leave the 9y alone
8x-9y=11
-8x -8x
-9y=11-8x
Now you have to move the -9, so the inverse of multiplying is dividing so you divide -9.
-9y/-9= 11/-9 -8x/-9
since you can't have negative as a denominator it would be:
y= -11/9+8x/9
<span>You have to change the signs</span>
