Question

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

Answer 1

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

Answer 2

View the graph for a visual

Explanation: