Answer :
absolute maximum = 3.033
absolute minimum = -1.846
What are the absolute maximum and minimum?
A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.
f(x) = x[tex]e^{-x^{2}/50 }[/tex] , [−2, 10]
f'(x) = x[tex]e^{-x^{2}/50 }[/tex] (-2x/50) + [tex]e^{-x^{2}/50 }[/tex] (1) = 0
-2[tex]x^{2}[/tex]/50 + 1 = 0
2[tex]x^{2}[/tex]/50 = 1
2[tex]x^{2}[/tex] = 50
[tex]x^{2}[/tex] = 25
x = +5 , -5
f(-2) = -2 [tex]e^{-2^{2} /50}[/tex] = -1.846
f(10) = 1.3353
f(5) = 3.033
absolute maximum = 3.033
absolute minimum = -1.846
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