Find the absolute maximum and the absolute minimum of the given function on the given interval f(x)=xe^x/2 on [-3,1]

Question

asked Jul 10, 2022 55.7k views

2 Answers

Jamie Barker · Answer 1 · 2022-07-13T07:37:35+0000

Answer:

Explanation:

$f(x)=xe^{(x)/(2) } \\f'(x)=x*(1)/(2) e^{(x)/(2) } +e^{(x)/(2) } =e^{(x)/(2) } ((x)/(2) +1)\\$

f'(x)=0, gives x=-2

we find f(x) at x=-3,-2,1

f(-3)=-3e^(-3/2)≈-0.67

f(-2)=-2e^(-2/2)=-2e^{-1}=-2/e≈-0.74

f(1)=1 e^(1/2)=√e≈1.65