Math, Calculus, Maximum/Minimum of a function help

luuu

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Determine the maximum and minimum value of the function f(x)=-xe^x+2

I've included a picture of what i've done so far, but i'm really lost and just guessing. Thank you soo much.
11117897_10202683245682048_1615543252_n.jpg
 
Determine the maximum and minimum value of the function f(x)=-xe^x+2

I've included a picture of what i've done so far, but i'm really lost and just guessing. Thank you soo much.
View attachment 5184

So, for the first derivative set to zero, you got

0 = -x(e^x) - 1(e^x); You stated e^x > 0.

Then, factoring,

0 = (-e^x)(x + 1)

What solution remains?

Ans: x = -1

Try graphing this function and see what is going on.

Hope that helps.
 
Most of your work is correct. You used the product rule and arrived at the first derivative of -xex - ex or, if you factor out a -ex​, it would be -ex(x+1).

The next step, and it looks like you tried this but got a little confused here, is to set the derivative equal to zero. By the zero product principle, that means that either: -ex = 0 or x+1 = 0.

As you noted, ex is always greater than zero, so that cannot be a solution. Therefore, the only critical point of your function is x+1 = 0 or x= -1.

Armed with this knowledge, you must now find out whether the critical point is a local maximum, a local minimum, or neither. You should be able to do that fairly easily.
 
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