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Differentiate the equation y^2 + y = x^3 + 2x

To answer this question you must use implicit differentiation due to there being both x and y terms. Consequently you must differentiate each term individually as you would usually (by multiplying by the pow...
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Answered by Daisy W. • Maths tutor
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solve the simultaneous equation; x^2+y^2=10 2x+y=5

When dealing with a linear and quadratic simultaneous equation, it is best to use subsitution to approach it.I take the linear equation and put it in terms of one variable. In this case, to avoid fractions i...
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Answered by Sinead O. • Maths tutor
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How to solve rates of change questions?

If the question is about something losing value, for example a cars value depreciates at a rate of 30% a year after 4 years how much will the car be worth? You are also given that at year 0 it was worth £10,...
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Answered by Emma W. • Maths tutor
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A curve has equation y = 20x −x^2 −2x^3 . Find its stationary point(s).

Differentiate the equation.Let the derivative equal to 0 and get x.Substitute the value of x into the original equation to get y.
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Answered by Ruonan L. • Maths tutor
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f(x) = 2x3 – 5x2 + ax + 18 where a is a constant. Given that (x – 3) is a factor of f(x), (a) show that a = – 9 (2) (b) factorise f(x) completely. (4) Given that g(y) = 2(33y ) – 5(32y ) – 9(3y ) + 18 (c) find the values of y that satisfy g(y) = 0, givi

a) 54-45+3a+18=0 3a+27=0 3a=-27 and thus a=-9b) 2x^3 – 5x^2 -9x + 18 = (x-3) (2x^2 +bx-6)to find b ; collect the x^2 terms so bx^2-6x^2=-5x^2 and thus b=1c) when comparing f(y) and f(x) we see that x=3^2yf(x...
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Answered by Akrit K. • Maths tutor
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