Determine the maximum and minimum value of the function f(x)=-xe^x + 2.
2 answers
Forget the calculus, sketch a graph.
-10 2.0005
-3 2.14
-2 2.27
-1 2.4 maximum
-0.5 2.3
0 2
1 -.72
2 -12.8
10 -220,263 minimum as x -->oo
derivative
y' = -[ xe^x + e^x]
= -e^x [x+1]
so max or min at x = -1
second derivative
y" = - [e^x(1)+(x+1)e^x]
= -e^x [ x+2 ]
if x = -1
then = -(1/e)(1)
negative so maximum
-3 2.14
-2 2.27
-1 2.4 maximum
-0.5 2.3
0 2
1 -.72
2 -12.8
10 -220,263 minimum as x -->oo
derivative
y' = -[ xe^x + e^x]
= -e^x [x+1]
so max or min at x = -1
second derivative
y" = - [e^x(1)+(x+1)e^x]
= -e^x [ x+2 ]
if x = -1
then = -(1/e)(1)
negative so maximum