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Find the stationary point of the curve y=3x^2-2x+2 and state the nature of this stationary point.

The stationary point is a minimum point. I will run through the working out for the question using the whiteboard in the session as it is difficult to demonstrate without relevant formatting.
WL
Answered by William L. • Maths tutor
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The alkanes and the alkenes are examples of homologous series of compounds. Name 3 properties of a homologous series.

There are a range of answers you could give: Homologous series' are chemically similar or chemically the same or react in the same way. They contain the same functional group, the same general formula (e.g. ...
UD
Answered by Ursula D. • Chemistry tutor
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Explain why the equation tanx + cotx = 1 does not have real solutions.

First of all, we need to express tangent and cotangent in terms of sine and cosine using the identities: tanx = sinx / cosx and cotx = cosx / sinx. Substituting these expressions into the initial equation we...
SV
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Differentiate the function y = (x^2)/(3x-1) with respect to x.

This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2], =[x(3x-2)]/[(3x-1)^2]
TS
Answered by Ted S. • Maths tutor
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A curve has equation y = x^3 - 3x^2 -24x + 5, find the x co-ordinates of the two stationary points of the curve and hence determine whether they are maximum or minimum points.

y = x 3 - 3x 2 - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x 2 - 6x -24 = 0 -> x 2 - 2x - 8 = 0 -> (x+2)(x-4) = 0Therefore the coordinates of the stationary p...
TS
Answered by Ted S. • Maths tutor
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