Mathematical Methods — Question 4

QCAA 2021, Paper 1 · 1 mark

Q4 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 4

The second derivative of the function

f(x)

is given by

f''(x)=\frac{2x}{1+x^2}.

The interval on which the graph of

f(x)

is concave up is

(A)

x<0

(B)

x\le0

(C)

x>0

(D)

x\ge0

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

Because

1+x^2>0

for all real

x

f''(x)>0

exactly when

x>0

Selects option C.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.