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1 year ago

Find the minimum value if f(x) = xe^x over [-2,0]

Mathematics

1 answer:

SashulF [63]1 year ago

6 0

Given function:

$f(x)=xe^x$

The minimum value of the function can be found by setting the first derivative of the function to zero.

$f^{\prime}(x)=xe^x+e^x$ $\begin{gathered} xe^x+e^x\text{ = 0} \\ e^x(x\text{ + 1) = 0} \end{gathered}$

Solving for x:

$\begin{gathered} x\text{ + 1 = 0} \\ x\text{ = -1} \end{gathered}$ $\begin{gathered} e^x\text{ = 0} \\ \text{Does not exist} \end{gathered}$

Substituting the value of x into the original function:

$\begin{gathered} f(x=1)=-1\times e^{^{-1}}_{} \\ =\text{ -}0.368 \end{gathered}$

Hence, the minimum value in the given range is (-1, -0.368)

You might be interested in

What is the interquartile range of this set of data? 15, 19, 20, 25, 31, 38, 41

Irina18 [472]

First, you have to find the median, which is the number in the middle: 25

Then cut the data in half by the median, so your new data sets are
15,29,20
and
31,38,41

Now you find the median of both of those sets, which is 29 and 38.

The interquartile range is the difference between the numbers, so 38-29 = 9.

8 0

3 years ago

What is the distance covered by a train while slowing down from

alukav5142 [94]

Answer:

The distance covered is 113.75 m

Step-by-step explanation:

As per the question:

The initial velocity of the train, v = 20 m/s

The final velocity of the train, v' = 6 m/s

Uniform deceleration, a = 1.6 $m/s^{2}$

Or uniform acceleration, a = - 1.6 $m/s^{2}$

<em>Here, the body decelerates, i.e., slows down at a uniform rate thus we take acceleration with negative sign.</em>

Now, to find the distance covered, s:

Using the eqn of Kinemetics:

$v'^{2} = v^{2} + 2as$

$6^{2} = 20^{2} + 2(- 1.6)s$

$36 - 400 = - 3.6s$

$s = \frac{- 364}{- 3.6} = 113.75\ m$

5 0

3 years ago

last weekend, 5% of the tickets sold at sea world were discount tickets. If sea world sold 60 tickets in all, how many discount

Ronch [10]

The percent proportion is a/b = p/100, where p is the percentage of the total fraction on the left side of the equation that you are trying to figure out.

We know that p=5, because p represents percentage, and the percentage 5% is equal to the fraction 5/100. Also, we know that 60 = b, or the denominator as this is the entire portion that we are trying to figure out.

a/60=5/100

Now, we need to use cross products, or multiplying the numerator of one fraction by the denominator of the other, and setting them equal to one another.

100 * a = 60 * 5

If we simplify by multiplying, then we get the equation:

100a = 300

When we divide the variable by the coefficient, we get the equation

a=3

Therefore, sea world sold 3 discount tickets.

5 0

2 years ago

Transform the Cartesian (rectangular) equation to a polar equation: x = -9. The selected answer is incorrect.

nika2105 [10]

Answer:

Solution : Option C

Step-by-step explanation:

We have the equations r² = x² + y², x = r cos(θ), and y = r sin(θ) that can be used to solve this problem. In this case we only need the second two equations ( x = r cos(θ), and y = r sin(θ) ) as we don't need to apply the concept of circles etc here.

Given : x = - 9,

( Substitute r cos(θ) for x )

r cos(θ) = - 9,

r = - 9 / cos(θ)

( Remember that sec is the reciprocal of cos(θ). Substitute sec for 1 / cos(θ) )

r = - 9 sec(θ)

Therefore the third option is the correct solution.

6 0

3 years ago

I need help anyone can help me? I’ll mark ya braninly

Oksana_A [137]

Answer:

You are more likely to grab a red marble. You are less likely to grab a green marble.

Step-by-step explanation:

6/16 is greater than 5/16. The bigger the number, the higher the probability.

Have a great day!

5 0

2 years ago