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A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.

(a) i) dy/dx= 2x-2-12x -1/2 ii) d 2 y/dx 2 = 2+6x -3/2 (b) Substitute x=4 into dy/dx= 2x-2-12x -1/2 Show that dy/dx= 0 and state 'hence there is a stationary point' (c) Substitute x=4 into d 2 y/dx 2 = 2+6x ...
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What was the most significant reason for the success of the First Crusade?

On July 15th 1099 Jerusalem, recently captured by the Fatimids of the Egyptian Sultan, Al-Musta'li, fell to the crusaders. With their victory, three years of campaign came to a victorious end; the assurances...
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Describe the Cognitive Interview. (6 marks).

The cognitive interview is an interview technique used in order to aid memory and improve accuracy of eye witness statements. The interview consists of four aspects: 'recall everything', 'reverse the order',...
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f ( x ) = 2 x ^3 − 5 x ^2 + ax + a. Given that (x + 2) is a factor of f ( x ), find the value of the constant a. (3 marker)

If x+2 is definitely a factor, that means when we sub x=-2 in, we should get 0 at the end. So 2(-2)^3 - 5(-2)^2 + a(-2) + a = 0So -16 -20= aso a = -36
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What are the key stages in phagocytosis?

First, the phagocyte (a specialised type of white blood cell) will recognise the pathogen by a process called chemoattraction -- this is essentially where the phagocyte 'follows' a chemical trail left by the...
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