Mathematical Methods — Question 16

QCAA 2021, Paper 1 · 4 marks

Q16 · 2021 · Technology-freeComplex familiar4 marks

QUESTION 16 (4 marks)

A tangent is drawn at the point

(1,e)

on the graph of the function

y=e^{2-x}

as shown. Determine the area of the shaded triangle.

WORKED SOLUTION

4 marks

ANSWER

2e

square units

Worked solution

y'=-e^{2-x}

, so the gradient at

(1,e)

-e

. The tangent is

(y-e)=-e(x-1)

. Its intercepts are

(2,0)

and

(0,2e)

, hence

\text{Area}=\frac12(2)(2e)=2e\text{ units}^2.

correctly determines the derivative

[1 mark]

determines equation of tangent

[1 mark]

determines x- and y-intercepts

[1 mark]

determines area of triangle

[1 mark]

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

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