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il63 [147K]
3 years ago
10

Xe^(-x^2/128) absolute max and absolute min

Mathematics
1 answer:
adoni [48]3 years ago
6 0
f(x)=xe^{-x^2/128}
\implies f'(x)=e^{-x^2/128}+x\left(-\dfrac{2x}{128}\right)e^{-x^2/128}=\left(1-\dfrac1{64}x^2\right)e^{-x^2/128}

Extrema can occur when the derivative is zero or undefined.

\left(1-\dfrac1{64}x^2\right)e^{-x^2/128}=0\implies 1-\dfrac1{64}x^2=0\implies x^2=64\implies x=\pm8

Maxima occur where the first derivative is zero and the second derivative is negative; minima where the second derivative is positive. You have

f''(x)=-\dfrac1{32}xe^{-x^2/128}+\left(1-\dfrac1{64}x^2\right)\left(-\dfrac{2x}{128}\right)e^{-x^2/128}=\left(-\dfrac3{64}x+\dfrac1{4096}x^3\right)e^{-x^2/128}

At the critical points, you get

f''(-8)=\dfrac1{4\sqrt e}>0
f''(8)=-\dfrac1{4\sqrt e}

So you have a minimum at \left(-8,-\dfrac8{\sqrt e}\right) and a maximum at \left(8,\dfrac8{\sqrt e}\right).

Meanwhile, as x\to\pm\infty, it's clear that f(x)\to0, so these extrema are absolute on the function's domain.
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Could someone explain how they get the answer for this?
jarptica [38.1K]

Answer:

40°

Step-by-step explanation:

The reference angle is the positive acute angle created by the terminal arm and the x-axis.

The highlighted red in the picture below shows what we're looking for.

The arm rotated 220° (but 'backwards' so the value given is negative).

|-220°| - 2(90°)          <= Subtract two right angles for two quadrants

= 220° - 2(90°)

= 220° - 180°

= 40°

Therefore, the reference angle is 40°.

If you got 50°, you probably calculated the angle with the terminal arm and the y-axis. Remember to always use the nearest side of the x-axis!

4 0
3 years ago
150 is 100% of what number?
andriy [413]

Answer:

150 is 100% of 150

Steps to solve "150 is 100 percent of what number?"

We have, 100% × x = 150

or,

100

100

× x = 150

Multiplying both sides by 100 and dividing both sides by 100,

we have x = 150 ×

100

100

x = 150

If you are using a calculator, simply enter 150×100÷100, which will give you the answer.

3 0
2 years ago
Please help me please please please.
faust18 [17]
Which one you need G!?!?
4 0
3 years ago
List at least two advantages each of using a credit card and using cash.
Sonbull [250]
Credit Cards: You don't have to worry about how much cash you have at hand. You can get money when you need it.

Money: You won't overspend. You won't have to worry about fees.
5 0
3 years ago
Read 2 more answers
5x+14&lt;4 or -2(x-8)&lt;-2
Kitty [74]

Answer:

Step-by-step explanation:

5x+14<4 or -2(x-8)<-2

    -14 -14      -2x+16<-2

5x<-10                -16  -16

÷5  ÷5           -2x<-18

x<-2              ÷-2   ÷-2

                     x>9   (sign changes because you divide by a negative number)

x<-2 or x>9

7 0
3 years ago
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