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1. Consider the curve with equation x

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IB Questionbank Mathematics Higher Level 3rd edition 1

1. Consider the curve with equation x2 + xy + y2 = 3.

(a) Find in terms of k, the gradient of the curve at the point (−1, k).

(5)

(b) Given that the tangent to the curve is parallel to the x-axis at this point, find the value of k.

(1) (Total 6 marks)

2. Find the gradient of the curve exy + ln(y2) + ey = 1 + e at the point (0, 1).

(Total 7 marks)

3. Find the gradient of the tangent to the curve x3 y2 = cos (πy) at the point (−1, 1).

(Total 6 marks)

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