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The first step is to recall the formula for arithmetic progressions: u(n) = a + (n-1)d We can then put all the information given in the question into this so u(12) = 66.5 = a + 11d and u(19) = 98 = a ...
Finding the gradient (m): The gradient is the change in y-axis over the change in x-axis Δy = -10-4= -14 Δx = 12-5=7 Δy/Δx = -14/7 = -2 Ac...
f(x) = 3x^3 + 2x^2 - 8x + 4
f(2) = 3(2)^3 + 2(2)^2 - 8(2) + 4
f(2) = 3(8) + 2(4) - 8(2) + 4
f(2) = 24 + 8 - 16 +4
f(2) = 20
a) By simple parametric differentiation of each term, dy/dx = 2x^2 + 2x b) The condition for a turning point is the gradient (dy/dx) at that point is zero. 0 = x(2x + 2) so either x=0 or 2x+2=0. Therefore...
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