更新1:
This student has not been taught calculus. I think his teacher will not expect his answer by using calculus. Thx again.
Give: y=x^2/e^x, 0<x<5. What is the largest possible value of y? (no dif. is allowed) This is IB maths quiz. Thanks for teaching .?
回答 (1)
2015-12-06 9:41 am
y=x²/e^x
y'=(2x e^x-x² e^x)/e^(2x)
=(2x -x²)/e^x
Let y'=0,then 2x -x²=0
x(x-2)=0
x=0(rej.) or 2
y(0)=(0)²/e^0=0
y(2)=(2)²/e^(2)=0.5413411...
y(5)=(5)²/e^(5)=0.1684867...
So the largest possible value of y is 4/e²
y'=(2x e^x-x² e^x)/e^(2x)
=(2x -x²)/e^x
Let y'=0,then 2x -x²=0
x(x-2)=0
x=0(rej.) or 2
y(0)=(0)²/e^0=0
y(2)=(2)²/e^(2)=0.5413411...
y(5)=(5)²/e^(5)=0.1684867...
So the largest possible value of y is 4/e²
收錄日期: 2021-04-18 14:09:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20151206010437AA5J9OA