(b) sin 4x/x3 1 (a) Differentiation - Product Rule.
Figure 1 shows the graph of equation y = f(x).
The points P (– 3, 0) and Q (2, – 4) are stationary points on the graph.
Sketch, on separate diagrams, the graphs of
(a) y = 3f(x + 2)
(b) y = |f (x)|
On each diagram, show the coordinates of any stationary points.
3. The area, A mm2, of a bacterial culture growing in milk, t hours after midday, is given by
A = 20e1.5t, t ≥ 0
(a) Write down the area of the culture at midday.
(b) Find the time at which the area of the culture is twice its area at midday. Give your answer to the nearest minute.3) Exponential functions.
4. The point P is the point on the curve x = 2 tan (y + π/12) with y-coordinate π/4
Find an equation of the normal to the curve at P.4) Normal to a curve.
5. Solve, for 0° ≤ θ ≤ 180°,
2cot2 3θ = 7 cosec 3θ - 5
Give your answers in degrees to 1 decimal place.5) Trig. equations
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