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What are the stationary points of the curve (1/3)x^3 - 2x^2 + 3x + 2 and what is the nature of each stationary point.

Firstly, a stationary point is a point on the curve where the gradient of the tangent line is equal to 0. Here, this occurs at points where the first derivative of f(x) = 1/3x 3 - 2x 2 + 3x + 2 is equal to z...
OM
Answered by Omar M. • Maths tutor
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Differentiate this equation: xy^2 = sin(3x) + y/x

y 2 + 2xy dy/dx = 3cos(3x) + 1/y - x/y 2 dy/dx thereforedy/dx = (3cos(3x) + 1/y - y 2 ​​​​​​) / (2xy + x/y 2 )
AE
Answered by Alexander E. • Maths tutor
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Can you please explain how to expand two brackets, eg. (3x-7)(5x+6)

When I am expanding brackets I use the acronym FOIL and simplify. You begin by multiply the first term (F) in each bracket, followed by multiplying the outside terms (O), then the inside terms (I) and finall...
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Given that cos(x) = 1/4, what is cos(2x)?

cos(2x) = 2cos 2 (x) - 1 This is the identity. Therefore we can substitute in 2[cos 2 (x)] to be 2 multiplied by (1/4) 2 .Therefore cos(2x) = 2(1/4)(1/4) - 1 = 2/16 - 1 = 2/16 - 16/16 =1/8 - 8/8 = -(7/8).Ans...
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Answered by Bhumi K. • Maths tutor
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Split (3x-4)/(x+2)(x-3) into partial fractions

(3x-4)/(x+2)(x-3) = A/(x+2) + B/(x-3)=> 3x-4 = A(x-3) + B(x+2)Let x = -2-10 = -5AA = 2Let x = 35 = 5BB = 1∴ (3x-4)/(x+2)(x-3) = 2/(x+2) + 1/(x-3)
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