Today we will do Q4, 5 and 8. We had already done Q6 and for Q7, it would require plotting on the graph paper, which I shall skip for technical reasons. We can discuss this at tuition class if we want to.
OK, Q4 first. It says:
A curve has the equation y = sin 2x – 3 cos x.
(i) Find the gradient of the curve when x = π/6
(ii) When x is increasing at a constant rate of 0.06 units per second, find the rate of change of y when x = π/6.
(i)When we see the question talking about gradients, we know we need to have the gradient function. The gradient function is the differential. Hence, we will need to find dy/dx.
Hence, if y = sin 2x – 3 cos x, then
When x = π/6
(ii) This second part is talking about rates of increase. This means that we have to go into rate of change which is always stated as:
Given that dy/dx = 2.5, and that dx/dt = 0.06 units per second, then
therefore,
Therefore, rate of change of y = 2.5 x 0.06 = 0.15 units per second.
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