Differentiation of exponential and logarithmic functions — Question 71

Original QCE Vault practice · 1 mark

Q71 · Practice questionTechnology-freeComplex familiar1 mark

QUESTION 71

For

f(x)=(x+1)e^{-x}

, the maximum value of

f

for

x\ge0

(A)

e^{-1}

(B)

1

(C)

2e^{-1}

(D)

2

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

f'(x)=-xe^{-x}

, which is non-positive for

x\ge0

. Hence the maximum occurs at

x=0

, where

f(0)=1

Selects the correct option.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.