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Please help me I don't think my answer is correct

Please help me I don't think my answer is correct-example-1
User Son
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1 Answer

3 votes

To find the derivatives we have to use the following property:


(d(uv))/(dx)=u^(\prime)v+uv^(\prime)

Then the first derivative will be:


y\text{ = 2xe}^(-x)


y^(\prime)\text{ = }2\mleft(e^(-x)-e^(-x)x\mright)

Now to find the second derivative we have to use the same derivative property with the part "-xe^-x. Thus:


y^(\doubleprime)=2(-2e^(-x)+xe^(-x))

Now we have to equal the equation to zero:


2(-2e^(-x)+xe^(-x))=0


-2e^(-x)+xe^(-x)=0


e^(-x)(x-2)=0_{}

The first solution will be:


e^(-x)=0


-x\text{ = ln 0}

ln 0 is undefined, so this answer is impossible.

The second solution will be:


x-2\text{ = 0}


x\text{ = 2}

Answer: x = 2.

User Chaviva
by
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