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**balliztiks** Hello. Need some awnsers to mark my practise exam papper. Please and thank you.

1. Differentiate each of the following with respect to x

a. 2x2-4x+3/x2

b. (4x3-2x2-1)5

c. (sin 4x) (e3x)

d. x+2/3x-1

2. if f(x) = e5x find f”(x)

3. if x and y are defined parametrically as x=cos (θ) and y = cosec (θ), find dy/dx

4. Find the point of inflection of the function described by f(x) x3–6x2+12x - 4

Apply an appropriate test to make sure it is a point of inflection you found.

5. The cost, $C of running a dinghy with a small out board engine is C = 8/v2 + v/27, where v(km/hr) is the constant speed for the journey.

At what speed (to 2 d.p.) should the dinghy be run for the most economical trip?

Find the cost.

Apply an appropriate test to make sure it is a minimum cost you found.

6. A curve is defined by the parametric equations x= 4t and y=t2-4

Find the equation of the tangent at the point where t=2

7. a large cube of ice is melting so that its volume, v, is decreasing at the rate of 60 cm3/s.

Find the rate at which each side, x, of the cube is decreasing at the moment when the length of each side is 20cm.

Thanks alot.