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Maths
A Level

f(x) = sinx. Using differentiation from first principles find the exact value of f' (π/6).

The derivative of the function where x=π/6 is defined asThe limit as h->0 of [sin(h+π/6)-sin(π/6)]/hUsing the double angle formula, sin(h+π/6) = sin(h)cos(π/6) + cos(h)sin(π/6) = √3sin(h)/2 + cos(h)si...

Answered by • Maths tutor
7259 Views

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

OM
Answered by Omar M. • Maths tutor
7334 Views

Differentiate this equation: xy^2 = sin(3x) + y/x

y2 + 2xy dy/dx = 3cos(3x) + 1/y - x/y2 dy/dx                   thereforedy/dx = (3cos(3x) + 1/y - y2​​​​​​) / (2xy + x/y2)

AE
Answered by Alexander E. • Maths tutor
3603 Views

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 fin...

Answered by • Maths tutor
4552 Views

Given that cos(x) = 1/4, what is cos(2x)?

cos(2x) = 2cos2(x) - 1 This is the identity. Therefore we can substitute in 2[cos2(x)] to be 2 multiplied by (1/4)2.Therefore cos(2x) = 2(1/4)(1/4) - 1 = 2/16 - 1 = 2/16 -...

BK
Answered by Bhumi K. • Maths tutor
8865 Views

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