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f(x) = (4x + 1)/(x - 2). Find f'(x)

Quotient rule: (vu' - uv')/v^2 u = 4x + 1 u' = 4 v = x - 2 v' = 1 Input into formula: [(x - 2)(4) - (4x + 1)(1)](x - 2)^2 Simplify: [4x - 8 -4x - 1]/(x - 2)^2 = -9/(x - 2)^2
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Answered by Salah S. • Maths tutor
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The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0. Find y: y = r sin(x) = 3a(1 + cos(x))(sin(x)) Differentiate y with respect to x dy/dx = 3a[(2cos(x) - 1)(cos(x) + 1)] = 0 Solve equation 2cos(x)- 1 = 0 cos(x) = 1/2 ...
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What characteristics might a perfectly competitive market have? Choose 3 (6 marks)

The first characteristic is that the products are homogenous, meaning there is little difference between the quality of the goods being sold by the individual firms. The second characteristic is that all the...
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Answered by Salah S. • Economics tutor
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Describe chemical test/s you could use to determine the identity of a carbonyl compound.

Use Brady's Reagent (2,4-DNPH) to test for the presence of the C=O bond in a carbonyl compound. The formation of a yellow precipitate indicates a positive test result. Then determine the melting point of the...
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Answered by Megan B. • Chemistry tutor
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When should you use the passé simple instead of the imparfait?/Quand devrais-tu utiliser le passé simple à la place de l'imparfait?

The passé simple is used to describe an action that belongs exclusively in the past and was not a habit, as in it happened only once in the past; whereas the imparfait is used to decribe an action that happe...
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Answered by Arthur B. • French tutor
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