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The curve C has the equation y=3x/(9+x^2 ) (a) Find the turning points of the curve C (b) Using the fact that (d^2 y)/(dx^2 )=(6x(x^2-27))/(x^2+9)^3 or otherwise, classify the nature of each turning point of C

(a)To find the turning points of a curve, need to solve dy/dx=0. Using the quotient rule one can differentiate y:y=f(x)/g(x) dy/dx=(f'(x)g(x)-f(x)g'(x))/(g(x)) 2 f(x)=3x, f'(x)=3, g(x)=(9+x 2 ), g'(x)=2x→ dy...
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Answered by Liora C. • Maths tutor
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Why do the trig addition formulae work?

Try differentiating:sin(x)cos(z-x)+cos(x)sin(z-x)with respect to x and for constant z, then simply the derivative you deduce, then integrate throughout the simplified equation. See what happens!
Answered by • Maths tutor
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Do the SUVAT equations work for acceleration that changes with time?

It depends on how much it changes. For instance, if some object does undergo as good as makes no difference constant acceleration, then the SUVAT equations apply quite well to the circumstances at play. If t...
Answered by • Physics tutor
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Why does 'x' need to be in radians to differentiate 'sin x'?

There are two definitions of the sine and cosine functions that anyone who uses contemporary maths, and I do mean anyone, uses silently or otherwise. The first is as follows:'Rotate the point (1,0) in Euclid...
Answered by • Maths tutor
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Pathogens are disease-causing organisms which can infect humans. Bacteria and viruses are two examples of pathogens. Explain the differences between bacteria and pathogens and give an example of each.

Bacteria:Contain naked DNA Have a cell wall, membrane and organelles - RibosomesAre cells Larger than virusesCan survive without living hostCan be treated with antibiotics example: Staphylococcus aureus Viru...
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Answered by Tabitha G. • Biology tutor
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