Hello. Need some awnsers to mark my practise exam papper. Please and thank you.
1. Differentiate each of the following with respect to x
c. (sin 4x) (e3x)
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.