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Contact [7]
3 years ago
5

9000000 in standard form

Mathematics
1 answer:
Andreyy893 years ago
8 0
The exponent form is 9.0x106.
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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
vichka [17]

Answer:

A(-1,0) is a local maximum point.

B(-1,0)  is a saddle point

C(3,0)  is a saddle point

D(3,2) is a local minimum point.

Step-by-step explanation:

The given function is  

f(x,y)=x^3+y^3-3x^2-3y^2-9x

The first partial derivative with respect to x is  

f_x=3x^2-6x-9

The first partial derivative with respect to y is  

f_y=3y^2-6y

We now set each equation to zero to obtain the system of equations;

3x^2-6x-9=0

3y^2-6y=0

Solving the two equations simultaneously, gives;

x=-1,x=3  and y=0,y=2

The critical points are

A(-1,0), B(-1,2),C(3,0),and D(3,2).

Now, we need to calculate the discriminant,

D=f_{xx}(x,y)f_{yy}(x,y)-(f_{xy}(x,y))^2

But, we would have to calculate the second partial derivatives first.

f_{xx}=6x-6

f_{yy}=6y-6

f_{xy}=0

\Rightarrow D=(6x-6)(6y-6)-0^2

\Rightarrow D=(6x-6)(6y-6)

At A(-1,0),

D=(6(-1)-6)(6(0)-6)=72\:>\:0 and f_{xx}=6(-1)-6=-18\:

Hence A(-1,0) is a local maximum point.

See graph

At B(-1,2);

D=(6(-1)-6)(6(2)-6)=-72\:

Hence, B(-1,0) is neither a local maximum or a local minimum point.

This is a saddle point.

At C(3,0)

D=(6(3)-6)(6(0)-6)=-72\:

Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.

At D(3,2),

D=(6(3)-6)(6(2)-6)=72\:>\:0 and f_{xx}=6(3)-6=12\:>\:0

Hence D(3,2) is a local minimum point.

See graph in attachment.

3 0
3 years ago
7y = 14 -28x to standard form
MissTica

Answer:

28x + 7y = 14.

Step-by-step explanation:

Just add the 28x to each side.

4 0
3 years ago
Read 2 more answers
Two column proofs Beginner's
Darina [25.2K]

LETS prove the 2nd part of the Question

Here concept of right angles is used

We can see BA is perp to BD

and BC is perp to BE

We have to prove angle 1 = angle 3

i will denote angle by a

therefore we need to prove a1 = a3

as BA is perp to BD hence angle between them will be 90 degree

a1 + a2 = 90 degree

Similarly BC is perp to BE

a2 + a3 = 90 degree

as both equations add up gives 90 degree so will equate them

a1 + a2 = a2 + a3

which means a1 = a3

Hence Proved

To learn more about Right Angles:

brainly.com/question/7116550

#SPJ1

3 0
1 year ago
If f(x) = 2x + 3 and g(x) =4x - 1, find f(4).
fomenos

Solve the "f" function with substitute 4 and solve the "g" function with what we get for the "f" function.

f(4) = 2(8) + 3

f(4) = 16 + 3

f(4) = 19

g(19) = 4(19) - 1

g(19) = 76 - 1

g(19) = 75

Best of Luck!

6 0
3 years ago
Find the y-intercept and the slope of the line<br><br> y=-x+7<br><br> y-intercept:<br> slope:
Ipatiy [6.2K]

Answer:

The y-intercept would be 7

The slope would be -1 or -1/1. They are both the same thing.

The slope is the number which is located directly to the left of the variable (the variable in this case is x, but in other situations it could be a totally different letter).

5 0
3 years ago
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