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The expansion of (1+x)^4 is 1 + 4x +nx^2 + 4x^3 + x^4. Find the value of n. Hence Find the integral of (1+√y)^4 between the values 1 and 0 (one top, zero bottom).

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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.

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