SOLUTION: Locate the critical points of the following function. Then use the second derivative test to determine whether they correspond to local maxima, local minima, or neither. f(x)=-e^

Algebra ->  Test -> SOLUTION: Locate the critical points of the following function. Then use the second derivative test to determine whether they correspond to local maxima, local minima, or neither. f(x)=-e^      Log On


   

Question 1155976: Locate the critical points of the following function. Then use the second derivative test to determine whether they correspond to local maxima, local minima, or neither.
f(x)=-e^x(x-3)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=-e%5Ex%28x-3%29
Derivative:
d%2Fdx%28-e%5Ex+%28x+-+3%29%29+=+-e%5Ex+%28x+-+2%29
=> critical points:
-e%5Ex+%28x+-+2%29=0 => only if %28x+-+2%29=0 =>x=2
second derivative:
f'%28x%29+=+-e%5Ex+%28x+-+1%29..........now, plug the three critical number x=2 into the second derivative
f'%28x%29+=+-e%5E2+%282+-+1%29
f'%28x%29+=+-e%5E2+%281%29
f'%28x%29+=+-e%5E2+

At 2, the second derivative is negative ( -e%5E2+). This tells you that f is concave down where x=2, and therefore that there’s a local+max at +2.

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-e%5Ex%2A%28x-3%29%29+


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


f%28x%29+=+-%28e%5Ex%29%28x-3%29?

or

f%28x%29=+-e%5E%28x%28x-3%29%29?

The solution from the other tutor uses the first interpretation, even though all the expressions she shows in her work are like the second.

If indeed the expression is supposed to be the second, then of course the answer is completely different....