1.9.16 Implicit differentiation (A-level only)

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Question 44

A curve has equation

y^2 = y e^{3x} + 2x

a.

Show that

\frac{dy}{dx} = \frac{3y e^{3x} + 2}{2y - e^{3x}}

[4]

b.

The curve crosses the $y$ -axis at the origin $(0, 0)$ and at a second point $P$ . The tangent to the curve at the origin and the tangent to the curve at $P$ meet at the point $R$ . Find the coordinates of $R$ .

[4]

1.9.16 Implicit differentiation (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Question 44

A curve has equation

y^2 = y e^{3x} + 2x

a.

Show that

\frac{dy}{dx} = \frac{3y e^{3x} + 2}{2y - e^{3x}}

[4]

b.

The curve crosses the $y$ -axis at the origin $(0, 0)$ and at a second point $P$ . The tangent to the curve at the origin and the tangent to the curve at $P$ meet at the point $R$ . Find the coordinates of $R$ .

[4]

1.9.16 Implicit differentiation (A-level only)

Question 44

1.9.16 Implicit differentiation (A-level only) Questions

1.9.16 Implicit differentiation (A-level only)

Question 44

1.9.16 Implicit differentiation (A-level only) Questions