The diagram above shows a sketch of the curve C with the equation .
(a) Find the coordinates of the point where C crosses the y-axis.
(b) Show that C crosses the x-axis at x = 2 and find the x-coordinate of the other point where C crosses the x-axis.
(c) Find .
(d) Hence find the exact coordinates of the turning points of C.
(Total 12 marks)
2. (a) By writing sec x as show that = sec x tan x.
Given that y = e2x sec 3x,
The curve with equation y = e2x sec 3x, – has a minimum turning point at (a, b).
(c) Find the values of the constants a and b, giving your answers to 3 significant figures.
(Total 11 marks)
3. A curve C has equation
y = x2ex.
(a) Find , using the product rule for differentiation.
(b) Hence find the coordinates of the turning points of C.
(d) Determine the nature of each turning point of the curve C.
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