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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 broaden...
SM
Answered by Silvia M. • Maths tutor
8809 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 side dy/dx = (x/(1+x^2)) tan(y) Now separate the variables such that the x terms are on one side with the dx, and the y terms are on the ...
CG
Answered by Christian G. • Maths tutor
6827 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.
WL
Answered by William L. • Maths tutor
3974 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]
TS
Answered by Ted S. • Maths tutor
7173 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 = 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
8428 Views