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Specialist Maths — Question 14

QCAA 2022, Paper 1 · 4 marks

Q14 · 2022 · Technology-freeSimple familiar4 marks

QUESTION 14 (4 marks)

The slope field for the differential equation dydx=−0.5(y−4)x,x≠0,\frac{dy}{dx}=\frac{-0.5(y-4)}{x},\qquad x\ne0, using −6≤x≤6-6\le x\le6 and −6≤y≤6-6\le y\le6 is shown.
Slope field for dy/dx=-0.5(y-4)/x with point A marked
a)
Determine the value of the slope at point A(−4,−2)(-4,-2).
[2 marks]
b)
Use the slope field to sketch the solution curve for the differential equation given that x=−6x=-6, y=3.5y=3.5.
[2 marks]
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