f(x)=e的x次方乘以(3-x²),x∈[2,5]

问题描述:

f(x)=e的x次方乘以(3-x²),x∈[2,5]
求函数的最值

f(x)=(3-x^2)e^x
=3e^x-x^2e^x
f'(x)=3e^x-2xe^x-x^2e^x=e^x(3-2x-x^2)
令f'(x)>0
即3-2x-x^2>0
x^2+2x-3