Mathematical Methods — Question 14

QCAA 2021, Paper 1 · 4 marks

Q14 · 2021 · Technology-freeSimple familiar4 marks

QUESTION 14 (4 marks)

Consider the function

f(x)=\ln(3x+4)

, for

x>-\dfrac43

Determine

f'(x)

[1 mark]

Determine the

x

-intercept of the graph of

f(x)

[2 marks]

Determine the gradient of the tangent to the graph of

f(x)

at the

x

-intercept.

[1 mark]

WORKED SOLUTION

4 marks

ANSWER

f'(x)=\dfrac{3}{3x+4}

; b)

(-1,0)

; c)

3

Worked solution

f'(x)=\frac{3}{3x+4}.

b) At the

x

-intercept,

0=\ln(3x+4)

, so

3x+4=1

and

x=-1

f'(-1)=\frac{3}{-3+4}=3.

correctly determines the derivative

[1 mark]

correctly determines the linear equation

[1 mark]

correctly determines the x-intercept

[1 mark]

determines the gradient at the x-intercept

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

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