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A curve has equation x^2 + 2xy – 3y^2 + 16 = 0. Find the coordinates of the points on the curve where dy/dx =0

We would do this by differentiating everything individually so to differentiate x 2 we multiply the x 2 by the power which is 2 and then take the power down by 1 to make 2x. To differentiate 2xy we would use...
TK
Answered by Tom K. • Maths tutor
5400 Views

Show, by counter-example, that the statement "If cos(a) = cos(b) then sin(a) = sin(b)" is false.

Let a=60 and b=300. Then cos(a)=cos(60)=0.5 and cos(b)=cos(300)=0.5, therefore cos(a)=cos(b). Then sin(a)=sin(60)=sqrt(3)/2 and sin(b)=sin(300)=-sqrt(3)/2, therefore sin(a)=sin(b) is incorrect. Therefore we ...
OG
Answered by Osian G. • Maths tutor
4862 Views

Differentiate y(x)=x^2 + 2x + 1, find the turning point and classify it as minimum or maximum.

dy/dx=2x + 2 Turning point is where dy/dx=0, so when x = -1 When x=-1, y=0. d^2y/dx^2=2 > 0 therefore minimum.
JF
Answered by John F. • Maths tutor
4541 Views

Differentiate (3x)e^(3x)

3e^3x + (9x)e^3x This is a good question because it involves the use of both the chain and product rules of differentiation, as well as the differential of e (all of which occur frequently in Maths A-level a...
JH
Answered by Joe H. • Maths tutor
4638 Views

Integrate 5cos(3x - 1) with respect to x

Firstly, we may simplify the expression by factoring out any constants. In this case 5 can be factored out. 5 ∫ cos(3x-1) dx For the integrand cos(3x -1), we can use a simple u-substitution. Where u = 3x -1 ...
RM
Answered by Rian M. • Maths tutor
6063 Views