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we first remember the double angle formula, a really important formula. cos(2x) = cos²(x) - sin²(x).We know that sin²(x) + cos²(x) = 1, therefore, cos(2x) = cos...

dy/dx = 3x² - 8x - 3
when dy/dx = 0 , 0 = 3x² - 8x - 3
Factorise : 0= (3x + 1)(x - 3)
when 3x+1 =0 , x = -1/3when x-3=0 , x =3
so x = -1/3 , 3co-ordinates are : (...

2^x = e^{ln(2^x)} = e^xln(2) , d/dx(e^xln(2)) = ln(2)e^xln(2) = ln(2)*2^x

let u=kx,du/dx=ky= 4 sin(u)dy/du= 4cos(u)
dy/dx= du/dx*dy/du = 4kcos(u) =4kcos(kx)

So with these kind of questions they tend to be more of a first part to a question, probably worth about two marks on an A Level exam.The first thing to spot with this question is that f(x) contains a pro...