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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...
LC
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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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...
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Differentiate y= (6x^2 - 5)^(3/2) with respect to x

Simplify the equation to y=u 3/2 where u = 6x 2 -5Use the chain ruledy/dx = dy/du x du/dxdy/du = (3/2)u 1/2 du/dx = 12x - 0Therefore dy/dx = (3/2)u 1/2 x 12xBut u = 6x 2 -5 so substitute that into the deriva...
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13/2 - 5/3 = ?

Change both the denominators to 6...Times 13/2 by 3 to get 39/6Times 5/3 by 2 to get 10/6 Then its 39/6 - 10/6 and then look at the numerator and work out 39-10 = 29The answer is therefore 29/6
PB
Answered by Patsy B. • Maths tutor
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