Verbal expression for 1/8y

Identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results

Andrews [41]

Answer:

Step-by-step explanation:

Given that,

g(x, y) = 5 - (x - 3)² - (y + 2)²

Let find the grad of the function,

The grad of a function is defined as

∇g= ∂g/∂x •i + ∂g/∂y •j + ∂g/∂z •k

∇g = gx•i + gy•j + gz•k

gx = -2(x-3) = -2x+6

gy = -2(y+2) = -2y -4

∇g = (-2x+6) •i + (-2y-4)•j

We have a maximum or a minimum If g conservative, then, ∇g = 0i +0j

Then comparing this to the grad of the function

(-2x+6) •i + (-2y-4)•j = 0i +0j

Then, -2x+6 = 0

2x=6

x = 3

Also, -2y-4=0

-2y=4

y = -2

Then, g(x, y) = 5 - (x - 3)² - (y + 2)²

g(x, y) = 5 - (3 - 3)² - (-2 + 2)²

g(x, y) = 5

So the critical point is (3, -2, 5)

gx =-2x+6

Second derivative of gx with respect to x

gxx=-2

gy=-2y-4

Second derivative of gy with respect to y

gyy=-2

Second derivative of gx with respect to y

gxy =0

d =gxxgyy - (gxy)²

Then, gyy=gxx

d = -2×-2 -0²

d = 4-0=4

Since d>0

Since d is greater than 0, then, it is not a chair points.

Then, since gxx=-2<0, gyy=-2<0

Cause the second derivative in x (or in y) is less than zero, then the point is relatively maximum

So the maximum point is (3, -2, 5).

6 0

2 years ago

Need help with this math problems

maxonik [38]

Budget; Fixed Costs are the answers!

8 0

3 years ago

Read 2 more answers

Hanna has 44 minutes to get ready for school she spends x minutes getting dress what's an expression that represent the number o

Goshia [24]

44-x= amount of time left

7 0

3 years ago

Suppose a random sample of 50 college students are asked to measure the length of their right foot in centimeters. A 95% confide

hichkok12 [17]

Answer:

A 99% confidence interval will be wider than a 95% confidence interval

Step-by-step explanation:

From the question we are told that

The 95% confidence interval for for the mean foot length for students at the college is found to be 21.709 to 25.091 cm

Generally the width of a confidence interval is dependent on the margin of error.

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

From the above equation we see that

$E \ \ \alpha \ \ Z_{\frac{\alpha }{2} }$

Here $Z_{\frac{\alpha }{2} }$ is the critical value of the half of the level of significance and this value increase as the confidence level increase

Now if a 99% confidence level is used , it then means that the value of

$Z_{\frac{\alpha }{2} }$ will increase, this in turn will increase the margin of error and in turn this will increase the width of the confidence interval

Hence a 99% confidence interval will be wider than a 95% confidence interval

5 0

2 years ago

Find the value of x - if x^3-7x² - x = 0<br>a) 17 (b) 71 c) 7<br>d) 1

S_A_V [24]

Answer:

x = 0

Step-by-step explanation:

$x^3-7x^2-x =0\\$

Take out common factor

$x(x^2-7x-1) = 0$

The factor inside the parenthesis cannot be factored

Since there is a common factor that we pulled out of the original equation,

set that x equal to zero and solve

$x = 0\\$ : Therefore x = 0

6 0

3 years ago