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Find the turning point of y = x + 1 + 4/x2 and describe the nature of the turning point

To find the turning point of the equation, it should be recognised that we desire the point at which the gradient is 0. The gradient is given by dy/dx and hence we differentiate the equation with respect to ...
AK
Answered by Animit K. • Maths tutor
11698 Views

Given y=2x(x^2-1)^5, show that dy/dx = g(x)(x^2-1)^4 where g(x) is a function to be determined.

y=2x(x 2 -1) 5 --> y=uv, where u=2x; v=(x 2 -1) 5 --> thus product rule required.u'=2v'=10x(x 2 -1) 4 Product rule: dy/dx = uv' + v'uTherefore: dy/dx = 2x(10x(x 2 -1) 4 ) + 2(x 2 -1) 5 g(x) = (22x 2 -2)
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Answered by Sean H. • Maths tutor
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Find the finite area enclosed between the curves y=x^2-5x+6 and y=4-x^2

Starting by factorising the curve equations: the first one factorises to y = (x-3)(x-2) and the second one becomes y=(2-x)(2+x). From this, a rough sketch of the curves can be drawn and it can be seen that f...
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Answered by Ruby N. • Maths tutor
4558 Views

Differentiate (3x^2-5x)/(4x^3+2x^2)

We can differentiate the expression using the quotient rule. If f(x)=u(x)/v(x) then f'(x)=(u'(x) v(x)-u(x) v'(x))/v(x)^2. In this case u(x)=3x^2-5x so u'(x)=6x-5 and v(x)=4x^3+2x^2 so v'(x)= 12x^2+4x. Using ...
AI
Answered by Andras Ivan A. • Maths tutor
5112 Views

How do I integrate by substitution?

Let's take for example the integral 5x 2 (x 3 -4) 4 dx. This is very difficult and not at all nice to expand in terms of x, so we can effectively "create" a new variable, u, and set it to equal x 3...
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Answered by Edward C. • Maths tutor
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