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2 years ago

For the polynomial function ƒ(x)= −2x2 − 4x + 16, find all local and global extrema.

Mathematics

1 answer:

rusak2 [61]2 years ago

7 0

For the given quadratic equation we only have a maximum at y = 18.

<h3>How to find the extrema of the given function?</h3>

Here we have:

$f(x) = -2x^2 - 4x + 16$

Notice that this is a quadratic equation of negative leading coefficient.

Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.

The vertex is at:

x = -(-4)/(2*(-2)) = -1

The maximum is:

$f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18$

If you want to learn more about quadratic equations:

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A manufacturer claims that fewer than 6% of its fax machines are defective. to test this claim, he selects a random sample of 97

AfilCa [17]

Let P be the population proportion, p be the sample proportion, n be the sample size.

A manufacturer claims that fewer than 6% of its fax machines are defective. It means P=0.06

Sample size n=97 and sample proportion p=0.05

The hypothesis to be tested is

H0: P ≥ 0.06 V/s Ha: P < 0.06

Here the hypothesis for testing population proportion we use z test statistics. Z test statistics is give by

Z = $\frac{p -p_{0}}{\sqrt{p_{0}(1-p_{0})/n}}$

Where p =sample proportion = 0.05

p0 = hypothesized proportion value =0.06

Using given values into test statistics we get

Z = $\frac{0.05 -0.06}{\sqrt{0.06(1-0.06)/97}}$

Z = -0.41

The p-value for left tailed alternative hypothesis is given by

P-value = P(z < z cal)

where zcal = Z test statistics value

Here zcal = -0.41

P-value = P(Z < -0.41)

Using z score table to find probability below z=-0.41

P-value = 0.3409

P-value for testing the given claim is 0.3409

3 0

4 years ago

Which table could NOT represent a function?

Cloud [144]

Answer:

The fourth one

Step-by-step explanation:

Just cause its right

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3 years ago

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Draw the graph of the equation: 1.5x+2y=3

Sati [7]

Answer:

Step-by-step explanation: Your supposed to move 1.5x to the other side of 2y. Then you have -1.5x on the right side. Divide all terms by 2 and you’ll get your equation in y=mx+b format. Hope this helps

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3 years ago

Question 9

Alenkasestr [34]

Answer:

$PX=4\\PY=4\sqrt{3}$

Step-by-step explanation:

Let $\angle PYZ=Q$

$\Rightarrow \angle XYP=90-\angle PYZ\\\angle XYP=90-\theta$

In the $\Delta PYZ$

$\tan\theta =\frac{opposite}{adjacent}=\frac{PZ}{PY}......(1)$

In the $\Delta YPX$

$\tan(90-\theta)=\frac{opposite}{adjacent}=\frac{PX}{PY}$

$\cot=\frac{PX}{PY}....(2)$

eqn(1) $\times$ eqn(2)

$\tan\times\cot\theta=\frac{PZ}{PY}\times\frac{PX}{PY}\\\\1=\frac{PZ\times PX}{PY^2}\ \ (as\ tan\theta\ =\frac{1}{\cot\theta})\\\\PY^2=PZ\times PX\\PY^2=12PX.......(3)$

Now in $\Delta XYP$

use Pythagorean theorem

$XY^2=PY^2+PX^2\\8^2=PY^2+PX^2\ \ (as\ XY\ =8)\\PX^2+PY^2=64\\\\PY^2=12PX\ \ (eqn(3)\\\\\Rightarrow PX^2+12PX=64\\\\PX^2+12PX-64=0\\\\PX^2+16-4PX-64=0\\\\(PX+16)(PX-4)=0\\\\PX=4,\ -16$