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^

Question 1156266: 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
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I interpreted this as (x-3)*e^x.

derivative is (x-3)(e^x)+e^x
set it equal to 0
e^(x)+(x-3+1)=0
e^x(x-2)=0
critical point at x=2
second derivative is (x-1)e^x, which is positive where x=2
it is a minimum
root is where x=3
Here is the plot for e^(x^2-3x)

Here x=3/2 is the minimum and y=0.1055 is the value.
f''(x)=4x^2-12x+11 (e^(x^2-3x)) which is positive when x=3/2
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