IB Maths AA SL AA 5.1 practice question

Paper 2, calculatorMedium6 marks

For $x\in\mathbb{R}$ let $f(x)=(x+2)e^{-x}$

(a)

Find $f'(x)$

[2]

(b)

Hence determine the coordinates of the local maximum of the curve $y=f(x)$ justifying that it is a maximum.

[4]