Differentiation of trigonometric functions and differentiation rules — Question 159

Original QCE Vault practice · 4 marks

Q159 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 159 (4 marks)

For

h(x)=\dfrac{\ln x}{x+1}

x>0

, determine the equation of the tangent to the graph of

h

x=1

WORKED SOLUTION

4 marks

ANSWER

y=\dfrac12(x-1)

Worked solution

h'(x)=\dfrac{(x+1)/x-\ln x}{(x+1)^2}

. At

x=1

h(1)=0

and

h'(1)=1/2

. Therefore the tangent is

y-0=\tfrac12(x-1)

Uses the quotient rule correctly.

[1 mark]

Determines the point on the curve at

x=1

[1 mark]

Determines the gradient at

x=1

[1 mark]

States the tangent equation.

[1 mark]

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

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