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Mariana [72]
1 year ago
5

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)

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(1 point) 6 cards are drawn at random without replacement from a standard deck. Be accurate to 7 decimal places. a) Find the pro
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Answer:

a) P=0.0000843

b) P=0.0000454

c) P=0.0066113

Step-by-step explanation:

6 cards are drawn at random without replacement from a standard deck.

a) We calculate the probability that all the cards are hearts.

We calculatethe number of possible combinations:

C^{52}_6=\frac{52!}{6!(52-6)!}=20358520

We calculate the number of favorable combinations:

C_6^{13}=\frac{13!}{6!(13-6)!}=1716

Therefore, the probability is

P=\frac{1716}{20358520}\\\\P=0.0000843

b) We calculate the probability that all the cards are face cards.

We calculatethe number of possible combinations:

C^{52}_6=\frac{52!}{6!(52-6)!}=20358520

We calculate the number of favorable combinations:

C_6^{12}=\frac{12!}{6!(12-6)!}=924

Therefore, the probability is

P=\frac{924}{20358520}\\\\P=0.0000454

c) We calculate the probability that all the cards are even.

We calculatethe number of possible combinations:

C^{52}_6=\frac{52!}{6!(52-6)!}=20358520

We calculate the number of favorable combinations:

C_6^{24}=\frac{24!}{6!(24-6)!}=134596

Therefore, the probability is

P=\frac{134596}{20358520}\\\\P=0.0066113

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Step-by-step explanation:

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Step-by-step explanation:

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Cross multiply
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