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How would this be solved: f(x) has a turning point at (0,2) and passes through (-1,3). Find F(x).     
Could you please help me with this question... The function f is defined by f(x) = 5 + 4x - x2. (a) Express f(x) in the form a + b(x+c) 2. I can do this... 9 - (x-2) 2...it is part (b) I am stuck with... (b) For what range of values of x is f(x) both negative and increasing? I thought that you would differentiate 5 + 4x - x2 and for an increasing function let it be > 0...but when I did this I got x < -2 and the answer is x<-1. Could you please explain why it is x < -1.     
Could you please help me with this question... Give that the magnitude of p = 4 and p.q = 8, show that p is perpendicular to (p - 2q). I often get stuck on proof questions...do you have any general advice?     
Wondering if you could help with two maths problems I have encountered whilst doing past papers. They are: 1. For what range of values of k does the equation x2 +y2 + 4kx - 2ky - k -2 = 0 represent a circle? Can this be worked out without using the formula x2 + y2 + 2gx + 2fy + c = 0, as I have been taught this formula isn't necessary. 2. Integrate between 1 and 0 (cos(3x) - sin(1/3x +1)) dx. I integrated the equation to 1/3sinx + 3cos(1/3x + 1), but then got a strange answer when I subbed in the limits.     
How do I integrate (x^2-2)(x^2+2)/x^2 dx?     
I've looked in my notes and I really can't do this question: If y= (x^3-4x+8)/2x, where x cannot equal 0, find dy/dx.     
Could you please explain the concept of using quadrants to find angles, as this is a type of question I frequently get wrong as I don't understand how to use it or how it works.     
Please help me with this question - I have never seen a question like this! If f: x → x / (x-3) where x is a real number and x cannot equal 3, find f (-1)     
Why is (1/3/4) or one over three quarters the same as (4/3) or four over three?     
I'm trying to get my 10 year old to understand how to work out this problem 27 is 9 of 30 -- x How can I explain how to do this? Thanks Michelle    
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