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Mathematical Methods — Question 7

QCAA 2021, Paper 2 · 1 mark

Q7 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 7

Determine

f(x)

, given

f'(x)=6x^2+\dfrac1{x^2}+\dfrac1x

and

f(1)=5

.

(A)

f(x)=2x^3+\dfrac{3}{x^3}+\ln(x)-1

(B)

f(x)=2x^3-\dfrac1x+\ln(x)+4

(C)

f(x)=2x^3-\dfrac1x+\dfrac{2}{x^2}+2

(D)

f(x)=2x^3+\dfrac{3}{x^3}+\dfrac{2}{x^2}-2

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

B

Worked solution

Integrating gives

f(x)=2x^3-1/x+\ln x+C

. Since

f(1)=2-1+C=5

,

C=4

.

Selects option B.

[1 mark]

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

View the full QCAA marking guide

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