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Show that x^2 - x +2 is positive for all values of x

(x-1/2) 2 = (x-1/2)(x-1/2)=x 2 -x+1/4, add 7/4 to get x 2 -x+2 therefore x 2 -x+2 = (x-1/2) 2 + 7/4 squared numbers always positive so (x-1/2) 2 >= 0 therefore (x-1/2) 2 + 7/4 is always positive
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Answered by Pearse M. • Maths tutor
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How should I structure my essay?

As much as you may not want to hear this, there is no absolute, correct way to structure an essay. The essay structure that you use really depends on the question that you are being asked. However, there are...
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Answered by Stephanie M. • History tutor
3189 Views

How to write an algebraic fraction in a given form e.g. (3+13x-6x^2)/(2x-3) as Ax + B + C/(2x-3) where A, B and C are natural numbers

I would break this down into simple steps: Step 1 - Equate the 2 expressions: (3 + 13x - 6x 2 ) / (2x - 3) = Ax + B + C / (2x - 3) Step 2 - Multiply both sides by the demoninator: 3 + 13x - 6x 2 = (2x - 3)*A...
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Answered by Alex T. • Maths tutor
4468 Views

I am struggling to with unseen organic chemistry mechanism. I don’t know where to begin drawing them.

The purpose of a mechanism in organic chemistry is to show the movement of electron density leading to the reaction. Keeping this in mind, when faced with the starting materials, the first thing to identify ...
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Answered by Darius S. • Chemistry tutor
2888 Views

Find the derivative of the function f:(0,oo)->R, f(x)=x^x.

The domain of the function allows us to write f(x)=x x as f(x)=e ln(x ^x) =e x ln( x) (since ln(x) is defined on (0,oo) only). Using the standard derivative rules we get f'(x)=e x ln(x) (x ln(x))'=e x ln(x) ...
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Answered by Andrei R. • Maths tutor
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