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Maths
A Level

Factorise 6x^2 + 7x - 3=0

In order to solve the equation, we need to find a way to break the '7x' term in the middle that allows factorisation. We also need to consider the fact that the last term '-3x' has a minus sign. This broa...

Answered by Silvia M. Maths tutor
7225 Views

Solve the differential equation (1 + x^2)dy/dx = x tan(y)

Firstly rearrange the equation so that only dy/dx is on the left hand sidedy/dx = (x/(1+x^2)) tan(y)Now separate the variables such that the x terms are on one side with the dx,...

Answered by Christian G. Maths tutor
5491 Views

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.

Answered by William L. Maths tutor
3061 Views

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]

Answered by Ted S. Maths tutor
5909 Views

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 = x3 - 3x2 - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x2 - 6x -24 = 0 -> x2 - 2x - 8 = 0 -> (x+2)(x-4) = 0Th...

Answered by Ted S. Maths tutor
6999 Views

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