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1. The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) d d y x (ii) d d 2 y x 2 (3) (b) Verify that C has a stationary point when x = 2 (2) (c) Determine the nature of this stationary point, giving a reason for your answer.

To differentiate use formula. multiply factor by power then minus one from power (where x is invloved) dy/dx = 12x^3 - 24x^2 d^2y/dx^2 = 36x^2 - 48x (this is just a further differentiation) b) to find statio...
EI
Answered by Elysa I. • Maths tutor
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What is the difference between mutually exclusive and indepedent events?

Let's say that we have two events and we'll call them event A and event B. If these events were mutually exclusive then these events would not be able to occur at the same time. For example, if Real Madrid a...
CS
Answered by Callum S. • Maths tutor
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What is the chain rule?

A special rule, the chain rule, exists for differentiating a function of another function (finding dy/dx). Consider the expression cos x 2 . We call such an expression a ‘function of a function’. We could id...
DM
Answered by Diego M. • Maths tutor
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Express √75 in the form of n√3 , where n is an integer. Using this information, solve the following equation: x√48 = √75 + 3√3 (4 marks)

√75 = 5√3, therefore x√48 = √75 + 3√3 x√48 = 5√3 + 3√3 x(√16 x √3) = 5√3 + 3√3 4x√3 = 5√3 + 3√3 4x√3 = (5 + 3)√3 4x√3 = 8√3 x√3 = 2√3 x = 2
AT
Answered by Alex T. • Maths tutor
8613 Views

Differentiate and factorise y = x^2(3x + 1)

Product rule: dy/dx = uv' + u'v dy/dx = 2x(3x + 1) + x^2(3) dy/dx = 2x(3x + 1) +3x^2 dy/dx = 6x^2 + 2x + 3x^2 dy/dx = 9x^2 + 2x dy/dx = x(9x + 2)
EJ
Answered by Ella J. • Maths tutor
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